
	Where results make sense

Topic: Cohomology of groups

Related Topics

Exponential generating function

Entire function

Davis, South Dakota

United Alternative

Rushville, Missouri

Dugong

Gene Brewer

Premier Automotive Group

Brandon Wilson

County Football Association

Six Flags Fiesta Texas

Emperor Shun

Kevin Carter

Janel Moloney

	Cohomology - Wikipedia, the free encyclopedia
		That is, cohomology is defined as the abstract study of cochains, cocycles and coboundaries.
		Cohomology can be viewed as a method of assigning algebraic invariants to a topological space that has a more refined algebraic structure than does homology.
		A cohomology theory is a family of contravariant functors from the category of pairs of topological spaces and continuous functions (or some subcategory thereof such as the category of CW complexes) to the category of Abelian groups and group homomorphisms that satisfies the Eilenberg-Steenrod axioms
	en.wikipedia.org /wiki/Cohomology (679 words)

	PlanetMath: algebraic geometry
		Computations in cohomology generally use the same tools as computations in cohomology in algebraic topology: spectral sequences, excision, the Mayer-Vietoris sequence, and so on, with the exception that trivial facts about one-point topological spaces are replaced with difficult algebraic facts (this observation is essentially due to Milne, in his book Étale Cohomology).
		Lie groups are an extremely interesting family of objects to study; they describe symmetry groups of real objects and have sufficient internal structure to have very interesting properties.
		Algebraic groups are essentially matrix group schemes, and as such allow the tools of algebraic geometry to be applied to their study.
	planetmath.org /encyclopedia/AlgebraicGeometry.html (2523 words)

	Algebraic topology
		Two major ways in which this can be done are through fundamental group s, or more general homotopy theory, and through homology and cohomology groups.
		The fundamental groups give us basic information about the structure of a topological space; but they are often nonabelian and can be difficult to work with.
		The free rank of the ''n -th homology group of a simplicial complex is equal to the n -th Betti number, so one can use the homology groups of a simplicial complex to calculate its Euler-Poincaré characteristic.
	www.nebulasearch.com /encyclopedia/article/Algebraic_topology.html (835 words)

	Group cohomology (Site not responding. Last check: 2007-11-06)
		A slight generalization of those representations are the G-modules: a G-module is an abelian group M together with a group action of G on M, with every element of G acting as an automorphisms of M.
		The collection of all G-modules is a category (the morphisms are group homomorphisms f with the property f(gx) = g(f(x)) for all g in G and x in M).
		Early recognition of group cohomology came in the Noether's equations of Galois theory (an appearance of cocycles for H
	www.sciencedaily.com /encyclopedia/group_cohomology (721 words)

	Cohomology of Algebraic Varieties. Algebraic Surfaces/Algebraic Geometry \| - Cohomology of Algebraic Varieties. ... (Site not responding. Last check: 2007-11-06)
		Cohomology of Groups Verlagstext As a second year graduate textbook, Cohomology of Groups introduces students to cohomology theory (involving a rich interplay between algebra and topology) with a minimum of...
		Cohomology of Finite Groups Verlagstext The cohomology of groups has, since its beginnings in the 1920s and 1930s, been the stage for significant interaction between algebra and topology and has led to the creation of important...
		Verlagstext The cohomology of groups has, since its beginnings in the 1920s and 1930s, been the stage for significant interaction between algebra and topology and has led to the creation of important...
	shop.booxtra.de /cohomology.asp (388 words)

	COHOMOLOGY OF 2-GROUPS
		Of course, the point about abelian groups is that the cohomology rings are generated in degrees 1 and 2 and the relations are well known.
		In this section is listed the representative, the images of the generators for the cohomology of G as elements in the polynomial ring which is the cohomology of the elementary abelian subgroup, and a list of the generators of the kernel of the restriction map.
		In the case that the essential cohomology is not zero then the essflag is still true provided the the annihilator of the essential cohomology has dimension equal to the p-rank of the center of the group.
	www.math.uga.edu /~jfc/groups/cohomology.html (3660 words)

	[No title]
		The cohomology of groups is one of those branches of mathematics which is regarded by many, even some of its most enthusiastic proponents, as a tool for other areas of study.
		First in algebra during the early part of the century, the low dimensional cohomology groups were used to classify objects such as projective representations [] and group extension [].
		As a ``theory'', the cohomology of groups was born in the attempt to understand geometric/topological phenomena.
	www.elsevier.com /homepage/saj/523281/h16.htm (684 words)

	Group cohomology (Site not responding. Last check: 2007-11-06)
		A slight generalization of those representations the G -modules: a G -module is an abelian group M together with a group action of G on M with every element of G acting as an automorphisms of M.
		The collection of all G -modules is a category (the morphisms are group homomorphisms f with the property f (gx) = g (f (x)) for all g in G and x in M).
		Cohomology of Finite Groups (Grundlehren Der Mathematischen Wissenschaften)
	www.freeglossary.com /Group_cohomology (762 words)

	Higher Non-Abelian Cohomology Of Groups (ResearchIndex)
		The first non-abelian cohomology of groups introduced by Guin is extended to any dimensions and for a substancially wider class of coe#cients called G-partially crossed P-modules.
		The first and the second non-abelian cohomologies of groups are described in terms of torsors and extensions of groups respectively.
		Higher non-abelian cohomology pointed sets are described in terms of cotriple right derived functors of the group of derivations with respect to the first contravariant variable.
	citeseer.ist.psu.edu /339561.html (270 words)

	Algebraic topology - LearnThis.Info Enclyclopedia (Site not responding. Last check: 2007-11-06)
		Two major ways in which this can be done are through fundamental groups, or more general homotopy theory, and through homology and cohomology groups.
		The free rank of the n-th homology group of a simplicial complex is equal to the n-th Betti number, so one can use the homology groups of a simplicial complex to calculate its Euler-Poincaré characteristic.
		Beyond simplicial homology, one can use the differential structure of smooth manifolds via de Rham cohomology, or Cech or sheaf cohomology to investigate the solvability of differential equations defined on the manifold in question.
	encyclopedia.learnthis.info /a/al/algebraic_topology.html (438 words)

	Kids.net.au - Encyclopedia Algebraic topology -
		Fundamental groups give us crucial information about the structure of a topological space, but they are often nonabelian and can be difficult to work with.
		Beyond simplicial homology, one can use DeRham cohomology[?] to investigate the differential structure of manifolds, or Cech or Sheaf cohomology to investigate the solvability of differential equations defined on the manifold in question.
		In particular, fundamental groups, homology and cohomology groups are invariants of the underlying topological space, in the sense that two topological spaces which are homeomorphic have the same associated groups.
	www.kids.net.au /encyclopedia-wiki/al/Algebraic_topology (367 words)

	55: Algebraic topology
		Cohomology theories are a slight change from homology theories in that the directions of some homomorphisms are reversed; they're roughly the dual groups of the homology groups.
		Homology groups are particularly well suited to computation via some inductive procedure: if a space is somehow pieced together from simpler spaces (as unions, say, or fibrations) then the homology theories of the large space reflect those of the smaller spaces, together with some algebraic information which indicates the nature of the piecing-together.
		Apart from homology groups and their kin, the principal algebraic tool used in topology is the set of homotopy groups of a space, and related concepts; in particular this includes the fundamental group (pi_1(X)) of a space.
	www.math.niu.edu /~rusin/known-math/index/55-XX.html (2581 words)

	Combinatorial Extension Cohomology I Groups - DuPre'e (ResearchIndex)
		A new method is proposed for calculating the measurable, continuous or differentiable cohomology of a group extension which involves deriving functional equations for the restrictions of cocycles to certain well-behaved subsets of its domain, and showing that the cocycle can be written as a certain sum of such restrictions.
		on the decomposition of 2 cocycles on a group extension.
		3 Cohomology of Topological Groups and Solvmanifolds (context) - Mostow - 1961
	citeseer.ist.psu.edu /dupre93combinatorial.html (504 words)

	[No title]
		Cohomology theory, as above, deducing the only ways to piece together A and G to make X. In principle -- and again, I stress I would not want to do this in any but the smallest cases -- one could follow this procedure to compute all the solvable groups of a given order.
		For example, let G be the group of two elements, and let A be C2 x C2, where G swaps the two generators of A (e1 and e2, say).
		Your question seems to imply that every group may be examined internally and decided to be a cohomology group or not (just as one might examine a group and decide if it is a solvable group or not, or decide if it is a nilpotent group or not).
	www.math.niu.edu /~rusin/known-math/97/coho.grp (3344 words)

	COHOMOLOGY OF 2-GROUPS -- SECOND RUN
		Depth-essential cohomology: The depth-essential cohomology is the intersection of the kernels of the restrictions of the cohomology ring to the centralizers of the elementary abelian subgroups of rank 2
		Automorphisms of cohomology: We determine the outer automorphism of all of the groups that are not abelian and calculate the maps on the cohomology ring induced by a set of generators for the outer automorphism group.
		Moreover the annihilator of the depth-essential cohomology is an ideal whose variety in the maximal ideal spectrum of the cohomology ring has dimension equal to the depth of the cohomology ring.
	www.math.uga.edu /~jfc/groups2/cohomology2.html (1207 words)

	Brian Parshall - Bibliography (Site not responding. Last check: 2007-11-06)
		Cohomology of finite groups of Lie type, II Algebra 45 (1977), 182-198 (with E. Cline and L. Scott).
		Cohomology, hyperalgebras, and representations, J. Algebra 63 (1980), 98-123 (with E. Cline and L. Scott).
		Cohomology of quantum groups: the quantum dimension, Canadian Journal of Mathematics 45 (6) (1993), 1276-1298 (with Jian-pan Wang).
	www.math.virginia.edu /~bjp8w/bibliography.htm (1083 words)

	Cohomology of groups of units of quaternion algebras and EO2-resolutions (Site not responding. Last check: 2007-11-06)
		Cohomology of groups of units of quaternion algebras and EO2-resolutions
		Cohomology of groups of units of quaternion algebras and EO
		They are to a large extent controlled by the continuous cohomology of the automorphism group
	www.maths.abdn.ac.uk /~stc2001/abstracts/Henn/Henn.html (351 words)

	Publications of Ken Brown
		The homology of Richard Thompson's group F, preprint, November 2004, to appear in the proceedings of the AMS special session on Topological Aspects of Group Theory (Nashville, October 2004).
		(Russian) [Cohomology of groups] Translated from the English and with a preface and an appendix by D. Fuks.
		Cohomology with free coefficients of the fundamental group of a graph of groups (with
	www.math.cornell.edu /~kbrown/publications.html (284 words)

	[Polycyclic] 8 Cohomology for pcp-groups (Site not responding. Last check: 2007-11-06)
		Cohomology records provide the necessary technical setup for the cohomology computations for polycyclic groups.
		The finitely generated abelian group should be realized as a factor of a free abelian group modulo a lattice.
		The natural applications of first and second cohomology group is the determination of extensions and complements.
	www.mathematik.tu-darmstadt.de /~nickel/polycyclic/polycyclic-htm/CHAP008.htm (708 words)

	Cohomology And Euler Characteristics Of Coxeter Groups (ResearchIndex) (Site not responding. Last check: 2007-11-06)
		Cohomology And Euler Characteristics Of Coxeter Groups (ResearchIndex)
		Abstract: this paper, we discuss the cohomology and the Euler characteristics of (finitely generated) Coxeter groups.
		The Euler characteristic is defined for groups satisfying a suitable cohomological finiteness condition.
	citeseer.lcs.mit.edu /1028.html (445 words)

	Mineyev Abstract (Site not responding. Last check: 2007-11-06)
		B.E.Johnson introduced the bounded cohomology of groups (though the term "bounded cohomology" came later) and characterized the amenable groups by vanishing of bounded cohomology.
		We present the following characterization of Gromov hyperbolic groups by bounded cohomology: a finitely presented group G is hyperbolic if and only if all 2-dimensional cohomology classes of G are bounded for all coefficients.
		This boundedness of cocycles for hyperbolic groups (for real coefficients) was claimed by Gromov and was used by Connes and Moscovici to prove the Novikov conjecture for hyperbolic groups.
	www.math.uiuc.edu /Colloquia/01FA/mineyev_aug30-01.html (170 words)

	PlanetMath: group cohomology
		Then there is a long exact sequence in cohomology:
		This is version 6 of group cohomology, born on 2003-08-08, modified 2004-06-04.
		(Group theory and generalizations :: Connections with homological algebra and category theory :: Cohomology of groups)
	www.planetmath.org /encyclopedia/Cohomology.html (98 words)

	Field Theory and Cohomology of Groups (Site not responding. Last check: 2007-11-06)
		From the cohomological point of view, the restriction is simple: it is immediate from the conjecture that the cohomology must be generated by elements in degree 1, with all relations appearing by degree 2.
		One aim of the proposed research is to answer the question in [Ga-M], and therefore to provide a group theoretic interpretation of Milnor's conjecture on the structure of absolute Galois groups.
		Because there are very few general statements on the structure of absolute Galois groups, and because the current research on the arithmetic of fields depends upon this structure, this work should prove to be useful.
	www.pims.math.ca /birs/workshops/2003.old/03rit305 (1017 words)

	[No title] (Site not responding. Last check: 2007-11-06)
		This is intended to mean the representation theory of finite groups and related finite dimensional algebras, cohomology of finite groups, and computer calculations in these areas.
		One of the strongest reasons for studying the cohomology of finite groups is its connections with the representation theory.
		Computations with specific groups have been at the core of these developments, and many of the theorems and conjectures in the subject have arisen this way.
	www.lehigh.edu /~dmd1/db74 (503 words)

	Ian Leary's publications (Site not responding. Last check: 2007-11-06)
		Some of the newer ones are available to download as gzipped dvi files from the Southampton pure group preprint server.
		A bound on the exponent of the cohomology of BC-bundles, Proceedings of the 1994 Barcelona Conference on Algebraic Topology Progress in Mathematics 136, Birkhäuser (1996) 255-260 MR97k:55018.
		The subring of group cohomology constructed by permutation representations (joint with D. Green and B. Schuster), Proc.
	www.maths.soton.ac.uk /staff/Leary/titles.html (455 words)

	Rational isomorphisms between K-theories and cohomology theories, by Eric M. Friedlander and Mark E. Walker (Site not responding. Last check: 2007-11-06)
		The well known isomorphism relating the rational algebraic K-theory groups and the rational motivic cohomology groups of a smooth variety over a field of characteristic 0 is shown to be realized by a map (the "Segre map") of infinite loop spaces.
		Moreover, the associated Chern character map on rational homotopy groups is shown to be a ring isomorphism.
		Since semi-topological K-theory and morphic cohomology can be formulated as the semi-topological singular complexes associated to K-theory and motivic cohomology, this criterion provides a rational isomorphism between the semi-topological K-theory groups and the morphic cohomology groups of a smooth complex variety.
	www.math.uiuc.edu /K-theory/0557 (192 words)

	Lokal abgelegte Preprints (Site not responding. Last check: 2007-11-06)
		Commutative algebra in the cohomology of groups (dvi)
		Cohomology of sporadic groups, finite loop spaces, and the Dickson invariants (dvi)
		Cohomology of Modules in the principal block of a finite group (dvi)
	www.math.uni-wuppertal.de /~top/Alle/Benson (75 words)

	Elliptic cohomology of the Classifying space of discrete groups (Site not responding. Last check: 2007-11-06)
		is a generalized cohomology theory and BG is the classifying space of a group G.
		(BG) is to consider the case of finite groups, and a ``natural'' second step is to study groups of finite virtual codimension.
		After a description of the elliptic cohomology of finite groups we shall consider the elliptic cohomology of the classifying space of groups of finite virtual codimension.
	www.maths.abdn.ac.uk /~stc2001/abstracts/Devoto/Devoto.html (139 words)

Try your search on: Qwika (all wikis)