
	Where results make sense

Topic: Cohomology

Related Topics

Cochain complex

Homotopic

Homological algebra

Algebraic topology

Fundamental group

Category theory

Alexander Grothendieck

Projective module

Exact sequence

Principal bundle

Projective space

Topology

Flag manifold

Saunders Mac Lane

Algebraic geometry

	PlanetMath: Lie algebra cohomology (Site not responding. Last check: 2007-11-07)
		Generalizing a bit, Lie algebra cohomology is just the cohomology of a particular kind of algebraic theory.
		The aim was to calculate the cohomology, in the topological sense, of a compact Lie group by using the finite-dimensional data of the corresponding Lie algebra.
		This is version 9 of Lie algebra cohomology, born on 2003-08-14, modified 2006-02-03.
	planetmath.org /encyclopedia/Cohomology2.html (647 words)

	COHOMOLOGY OF 2-GROUPS
		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.
		The cohomology rings of the nonabelian groups of orders 8,16, and 32 are stored in a workspace which is loaded into MAGMA before the computations of the cohomology rings of the groups of order 64 begin.
	www.math.uga.edu /~jfc/groups/cohomology.html (3660 words)

	Motivic Cohomology
		The collection of all the cohomology groups of a space forms a ring, and the same is true of the K-groups.
		Cohomology arises from cutting up a space into smaller pieces, whereas K-theory arises from consideration of larger objects called vector bundles over the space.
		A remarkable achievement of Suslin and Voevodsky is that, after making a standard modification of the motivic cohomology and singular cohomology, they were able to prove that the modified motivic cohomology of X and the modified singular cohomology of X(C) are in fact isomorphic.
	www.ams.org /ams/mathnews/motivic.html (1302 words)

	Cohomology Rings (Site not responding. Last check: 2007-11-07)
		Cohomology groups are collections of exterior forms, graded by their order (number of differentials, dz's) which are annihilated by the exterior derivative(s) and are taken modulo exterior derivatives of other forms; they are additive groups, i.e., groups with respect to addition.
		The cohomology ring (with an appropriately chosen multiplication) of Calabi-Yau varieties reflects the mirror and duality transforms when these varieties are used for compactifying string theories.
		This relation between cohomology groups and the moduli space is used to detect the critical regions of the latter, as in the framework of variable spacetime vacua, in which the string theory changes drastically as such critical regions are approached - in real spacetime.
	string.howard.edu /~tristan/Research/CohoRings.htm (418 words)

	Cohomology computations
		The nilradical of the cohomology ring of group nunber 79 is nilpotent of degree 6.
		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.
		In the cases that have been calculated, the depth-essential cohomology is a free module over the polynomial subring of the cohomology ring generated by the elements of a regular sequence of maximal length.
	www.math.uga.edu /~lvalero/cohointro.html (958 words)

	[No title]
		The reason for restricting to this case is that on the one hand it is a convincingl* y large family of examples, whilst on the other, it is possible to give a rather concrete vers ion of the proof in which the correspondence between topological and commutative algebraic struc *tures is highlighted.
		The cohomology ring H(G; k) is known explicitly for a large numbe *r of groups, and we tabulate some examples to bring the discussion down to earth.
		28 (19* 78) 57-83 [54]P.A.Symonds and T.Weigel "The cohomology* of analytic pro-p-groups." Proc.
	hopf.math.purdue.edu /Greenlees/guanajuato.txt (11564 words)

	Cohomology and homology (Site not responding. Last check: 2007-11-07)
		Cohomologies and homologies are often used to describe global properties of manifolds or other objects.
		A homology is defined as the duals of the cohomology.
		For the DeRham cohomology the corresponding (dual) homology is the homology of submanifolds.
	www.phys.uu.nl /~hofman/scriptie/duality/node51.html (582 words)

	PlanetMath: group cohomology (Site not responding. Last check: 2007-11-07)
		The following proposition is very useful when trying to compute cohomology groups:
		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.
	planetmath.org /encyclopedia/Cohomology.html (98 words)

	On the Eisenstein cohomology of arithmetic groups, Jian-Shu Li, Joachim Schwermer
		The cohomology $H ^* (\Gamma, E)$ of an arithmetic subgroup $\Gamma$ of a connected reductive algebraic group $G$ defined over some algebraic number field $F$ can be interpreted in terms of the automorphic spectrum of $\Gamma$.
		This pertains to regular Eisenstein cohomology classes attached to cuspidal automorphic representations whose archimedean component is tempered.
		This result is supplemented by a qualitative structural result in the description of the cohomology in higher degrees by means of regular Eisenstein cohomology classes.
	projecteuclid.org /Dienst/UI/1.0/Summarize/euclid.dmj/1084479321 (782 words)

	Weil-etale motivic cohomology, by Thomas H. Geisser (Site not responding. Last check: 2007-11-07)
		As a consequence, we get a long exact sequence relating Weil-etale cohomology to etale cohomology, show that for finite coefficients the cohomology theories agree, and with rational coefficients a Weil-etale cohomology group is the direct sum of two etale cohomology groups.
		In the second half of the paper we restrict ourselves to Weil-etale cohomology of the motivic complex.
		We show that for smooth projective varieties over finite fields, finite generation of Weil-etale cohomology is equivalent to Weil-etale cohomology being an integral model of l-adic cohomology, and also equivalent to the conjunction of Tate's conjecture and (rational) equality of rational and numerical equivalence.
	front.math.ucdavis.edu /ANT/0351 (156 words)

	Cohomology
		Given the generators C for cohomology, as either module generators or as ring generators, the function returns the list of degrees of the minimal generators.
		Given the projective resolutions P and Q of two modules M and N and the cohomology generators C of the cohomology module, Ext_B^ * (M, N), the function returns the chain map from P to Q that lifts the n^(th) generator of the cohomology module and has degree equal to the degree of that generator.
		Given the projective resolution P of a module and the cohomology generators C of the cohomology ring of that module, the function returns the chain map from P to P that lifts the n^(th) generator of the cohomology ring and has degree equal to the degree of that generator.
	www.umich.edu /~gpcc/scs/magma/text1010.htm (659 words)

	HOPF-CYCLIC COHOMOLOGY
		Hopf-cyclic cohomology was recently discovered by Connes and Moscovici (e.g., see this paper) while studying the noncommutative geometry of foliations.
		This construction parallels to some extent the fundamental result of differential geometry that the de Rham cohomology ring of a manifold is isomorphic to the cohomology ring of differential forms invariant under the action of a compact group (Theorem 2.3 in ``Cohomology theory of Lie groups and Lie algebras", Trans.
		The second part of the talk is concerned with special cases: cyclic homology and cohomology of algebras as Hopf-cyclic theory for the trivial Hopf algebra and coefficients, and Connes-Moscovici cyclic cohomology of Hopf algebras as Hopf-cyclic theory for one-dimensional but non-trivial coefficients.
	www.fuw.edu.pl /~pmh/seminar/sem02.html (1632 words)

	[No title]
		Such results are not common in the cohomology of finite groups, as the structure of * a group is usually far more rigid than its cohomology*.
		Hence we see that in the Cohen-Macaulay situation, there is universal detec* tion by accessible groups with non-trivial essential cohomology;* the usefulness of such* * a result is illustrated for example in the calculations of the mod 2 cohomology of the spor* *adic simple groups M11, M12 and O0N.
		Then its coho* mology is detected by restriction to the cohomology* of centralizers of elementary abel* ian subgroups of maximal rank in G. Next we introduce Definition 1.3: The group G is said to satisfy the pC condition if every element of order p * in G is central.
	hopf.math.purdue.edu /Adem-Karagueuzian/cmhess.txt (2993 words)

	[Polycyclic] 8 Cohomology for pcp-groups
		The algorithm for determining the first cohomology group is outlined in
		Cohomology records provide the necessary technical setup for the cohomology computations for polycyclic groups.
		The natural applications of first and second cohomology group is the determination of extensions and complements.
	www-groups.dcs.st-and.ac.uk /~gap/Manuals/pkg/polycyclic/htm/CHAP008.htm (648 words)

	Seminar on 2-Vector Bundles and Elliptic Cohomology, IV \| The String Coffee Table
		For the case of principal bundles this term was introduced by Toby Bartels, but the basic idea was considered before, in particular in form of the 2-vector (2-)bundles of BDR which I mentioned.
		The way I understand the Grojnowski stuff is that he describes a rational (or rather complex) elliptic cohomology as the global sections in a sheaf of chain complexes over an elliptic curve.
		Re: Seminar on 2-Vector Bundles and Elliptic Cohomology, IV I belive that it is unclear what the exact relation is between elliptic cohomology in the sense leading to tmf, and the 2-vector bundle approach of BDR.
	golem.ph.utexas.edu /string/archives/000741.html (2338 words)

	Harris, M. and Taylor, R.: The Geometry and Cohomology of Some Simple Shimura Varieties. (AM-151).
		The results represent a major advance in algebraic number theory, finally proving the conjecture first proposed in Langlands's 1969 Washington lecture as a non-abelian generalization of local class field theory.
		This book constructs a candidate for such a local Langlands correspondence on the vanishing cycles attached to the bad reduction over the integer ring of K of a certain family of Shimura varieties.
		And it proves that this is roughly compatible with the global Galois correspondence realized on the cohomology of the same Shimura varieties.
	pup.princeton.edu /titles/7235.html (303 words)

	Graduiertenkolleg Homotopy and Cohomology (Site not responding. Last check: 2007-11-07)
		The strategy of Homotopy Theory is to establish this invariance for as many properties as possible, and then exploit the invariance to obtain a classification.
		As the direct approach is typically prohibitively difficult, one uses cohomology to calculate these homotopy groups by indirect means.
		singular) cohomology and generalized cohomology theories, together with the associated ring structure and cohomology operations.
	www.math.uni-bonn.de /people/GRK1150 (413 words)

	Finite group cohomology (Site not responding. Last check: 2007-11-07)
		Its cohomology class is the distinguished element of H^1(Gamma, A).
		Return the cohomology class of the 1-cocycle alpha.
		Given a 1-cocycle on an induced Gamma-group A/B, return the the set of all non-cohomologous 1-cocycles on A, which induce to a cocycle in the cohomology class of alpha.
	www.math.lsu.edu /magma/text381.htm (984 words)

	MATH 7590 Cohomology Theory
		The focus of this course will be on cohomology theory, dual to the homology theory developed in MATH 7520.
		One reason to pursue cohomology theory is that the cohomology of a space may be given a natural ring structure.
		These considerations will be used to study the topology of manifolds, yielding a number of duality theorems also relating homology and cohomology, with a variety of applications.
	www.math.lsu.edu /~cohen/courses/PastSemesters/SPRING01/M7590b.html (351 words)

	Problems on elliptic cohomology (Site not responding. Last check: 2007-11-07)
		Prove that the integral elliptic cohomology introduced by Hopkins admits an orientation from MO8, the 7-connected bordism spectrum.
		Then on U intersect V intersect W, you have three ways to trivialize and you need a cocycle condition to hold relating the three different transtion functions.
		One of the standard ideas for how to build elliptic cohomology is to only require the cocycle condition to hold up to natural isomorphism rather than on the nose.
	claude.math.wesleyan.edu /~mhovey/problems/elliptic.html (402 words)

	cohomology -- general cohomology functor (Site not responding. Last check: 2007-11-07)
		ScriptedFunctor -- the class of all scripted functors
		HH^ZZ ChainComplex -- cohomology of a chain complex
		HH^ZZ ChainComplexMap -- cohomology of a chain complex map
	www.math.uiuc.edu /Macaulay2/Manual/0177.html (52 words)

	Amazon.com: Quantum Cohomology: Books: K. Behrend,C. Gomez,V. Tarasov,G. Tian,P.de Bartolomeis,B. Dubrovin,C. Reina,P. ... (Site not responding. Last check: 2007-11-07)
		Join Amazon Prime and ship Two-Day for free and Overnight for $3.99.
		The book gathers the lectures given at the C.I.M.E. summer school "Quantum Cohomology" held in Cetraro (Italy) from June 30th to July 8th, 1997.
		The lectures and the subsequent updating cover a large spectrum of the subject on the field, from the algebro-geometric point of view, to the symplectic approach, including recent developments of string-branes theories and q-hypergeometric functions.
	www.amazon.com /exec/obidos/tg/detail/-/3540431217?v=glance (566 words)

Try your search on: Qwika (all wikis)