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Topic: Cobordism

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	PlanetMath: oriented cobordism (Site not responding. Last check: 2007-10-06)
		Cobordism is an equivalence relation, and a very coarse invariant of manifolds.
		There is a cobordism category, where the objects are manifolds, and the morphisms are cobordisms between them.
		This is version 4 of oriented cobordism, born on 2003-09-05, modified 2004-10-01.
	planetmath.org /encyclopedia/Cobordant.html (104 words)

	Cobordism - Wikipedia, the free encyclopedia
		In mathematics, cobordism is a relation between manifolds, based on the idea of boundary.
		We can say that two manifolds M and N are cobordant if their union is the complete boundary of a third manifold L; L is then called a cobordism between M and N.
		Cobordism theory became part of the apparatus of the extraordinary cohomology theory, alongside K-theory.
	en.wikipedia.org /wiki/Cobordism (368 words)

	Algebraic Cobordism I, by Marc Levine and Fabien Morel (Site not responding. Last check: 2007-10-06)
		Algebraic Cobordism I, by Marc Levine and Fabien Morel
		We compute the algebraic cobordism of the base field k, and show that this is naturally isomorphic to the Lazard ring.
		Finally, we relate the algebraic cobordism of X to the classical Chow ring of X and with the Grothendieck group of algebraic vector bundles on X. 0547.bib (228 bytes)
	www.math.uiuc.edu /K-theory/0547 (129 words)

	Manchester Geometry Seminar (Site not responding. Last check: 2007-10-06)
		We study finite group actions on manifolds and global invariants of manifolds with such actions from the point of view of cobordism theory.
		In some particular cases (such as the actions with only isolated fixed points or with fixed submanifolds having trivial normal bundle) it is possible to give an explicit description of cobordism classes of manifolds admitting such an action, say in terms of characteristic numbers.
		These results extrapolate some classical facts from the cobordism theory, such as the Hattori--Stong theorem.
	www.ma.umist.ac.uk /tv/Seminar/2002-2003/panov.html (235 words)

	Cobordism (L24) (Site not responding. Last check: 2007-10-06)
		The idea of a cobordism first appeared in works of Poincare at the beginning of the last century.
		We say that two manifolds of the same dimension are (co)bordant if there is a manifold whose boundary is diffeomorphic to the disjoint union of the two given manifolds.
		For example, the two-dimensional torus is bordant to zero (i.e., to the empty set), while the real projective plane is not the boundary of any compact three-manifold.
	www.maths.cam.ac.uk /CASM/courses/descriptions/node26.html (178 words)

	Dec 08-12 VU Math Events (Site not responding. Last check: 2007-10-06)
		The cobordism theory of smooth high-dimensional sphere knots was completely solved (or at least turned into an algebraic problem) in the 1960s through the work of Kervaire, who showed that all even-dimensional knots are cobordant, and J. Levine, who showed that the cobordism type of an odd-dimensional knot is determined by its Seifert matrix.
		In fact, two odd-dimensional knots are cobordant if and only if their Seifert matrices satisfy a certain algebraic cobordism equivalence.
		We study both cobordism of disk knots and cobordism rel boundary, holding the boundary sphere knot fixed.
	math.vanderbilt.edu /~calendar/archive/2003/12-12.html (414 words)

	Complex cobordism of Hilbert manifolds with some applications to flag varieties of loop groups (ResearchIndex) (Site not responding. Last check: 2007-10-06)
		We develop a version of Quillen's geometric cobordism theory for infinite dimensional separable Hilbert manifolds.
		This cobordism theory has a graded group structure under the topological union operation and has pushforward maps for Fredholm maps.
		We define Euler classes for finite dimensional complex vector bundles and describe some applications to the complex cobordism of flag...
	citeseer.ist.psu.edu /315329.html (467 words)

	Projects in Topology, Geometry and Combinatorics, Department of Mathematics, Univ. of Manchester, UK
		COBORDISM THEORY: Cobordism theory is a way of organising and classifying manifolds whose stable tangent bundles admit additional structure.
		It originally flowered in the hands of Renee Thom and Jack Milnor during the early 1960s, and the study of complex cobordism energised homotopy theory for the next 20 years or so; it is now finding applications in quantum field theory.
		I have been involved with the development of complex cobordism, framed cobordism, and symplectic cobordism since 1966, and can supervise work on several problems which remain unsolved.
	www.ma.man.ac.uk /DeptWeb/Groups/Pure/TopologyProjects.html (1141 words)

	[No title]
		The former are defined in terms of oriented > cobordism theory, while the latter seems to be more closely related > to complex cobordism theory [via formal group laws].
		Your comments were very helpful, as were those of Mark Hovey, who assured me that after we invert the prime 2, oriented cobordism theory and spin cobordism theory become the same, while complex cobordism becomes almost the same.
		More precisely, we've got a spectrum MU for complex cobordism theory, and we've got a spectrum MSO for oriented cobordism, but localizing away from 2 MU becomes isomorphic to MSO wedged with the double suspension of MSO.
	www.math.niu.edu /~rusin/known-math/00_incoming/ellip_coho (735 words)

	Atlas: Complex cobordism of Hilbert manifolds with some applications to flag varieties of loop groups by A. Baker (Site not responding. Last check: 2007-10-06)
		This cobordism theory has a graded group structure under the topological union operation and has push-forward maps for Fredholm maps.
		We define Euler classes for finite dimensional complex vector bundles and describe some applications to the complex cobordism of flag varieties of loop groups.
		The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cabc-34.
	atlas-conferences.com /cgi-bin/abstract/cabc-34 (154 words)

	Lessons from Topological Quantum Field Theory
		Second, just as we can use any cobordism to represent a spacetime going from one space to another, we can use any operator to describe a process taking states of one system to states of another.
		However, this is true neither for the category of Hilbert spaces nor for the category of cobordisms.
		This may seem like a fine point, but it is important, and we shall explore its significance in detail in Section 3.
	math.ucr.edu /home/baez/quantum/node2.html (1456 words)

	Algebraic cobordism and degree formulas (Site not responding. Last check: 2007-10-06)
		(-), called algebraic cobordism, on the category of smooth varieties over a field k of characteristic zero.
		I will then prove the analogue of Quillen theorem that the algebraic cobordism ring of the point is the Lazard ring L and the fact that the algebraic cobordism ring of a smooth variety is generated over L by elements of non-negative degrees.
		This implies the generalised degree formula conjectured by Rost and needed in his approach to the Bloch-Kato conjecture at odd primes.
	www.maths.abdn.ac.uk /~stc2001/abstracts/Morel/Morel.html (97 words)

	Complex Cobordism and Stable Homotopy Groups of Spheres (Site not responding. Last check: 2007-10-06)
		The applications of this and related techniques to the existence of infinite families of elements in the stable homotopy groups of spheres are then indicated.
		Quillen's theorem that the complex cobordism ring is isomorphic to the Lazard ring is proved and Quillen's method of constructing the BP spectrum by means of an idempotent is given.
		The BP-theoretic analogue of the dual of the Steenrod algebra is described and then used to make computations of the stable homotopy groups of spheres in a range which is impressive at this stage of the book.
	www.math.rochester.edu /people/faculty/drav/mu.html (1161 words)

	Talk 3891 data/Fall_2001/1112 (Site not responding. Last check: 2007-10-06)
		Using the properties and construction of complex cobordism as a guide, Morel and I have defined the notion of an oriented cohomology theory on smooth schemes over a field k, and have constructed a universal such theory, called algebraic cobordism, in case k has characteristic zero.
		Using algebraic cobordism, one can lift divisibility properties of Chern numbers of compact complex manifolds to divisibility properties of Chern classes (in the Chow ring) of the virtual normal bundle of a projective morphism to smooth k-varieties.
		We will describe our construction of algebraic cobordism, its relationship to algebraic K-theory and the Chow ring, and sketch a proof of the degree formulas.
	www.math.duke.edu /mcal?abstract-3891 (127 words)

	Algebraic Aspects of the Theory of Product Structures in Complex Cobordism (ResearchIndex) (Site not responding. Last check: 2007-10-06)
		We show how to reduce this problem to the algebraic one in terms of the Hopf algebra S (the Landweber-Novikov algebra) acting on its dual Hopf algebra S with a distinguished \topologically integral" part that coincids with the coecient ring of the complex cobordism.
		We describe the formal group and its logarithm in terms of representations of S.
		1 Characteristic classes in cobordism and topological applicat..
	citeseer.ist.psu.edu /botvinnik01algebraic.html (499 words)

	Spin Cobordism Determines Real K-Theory - Hopkins, Hovey (ResearchIndex) (Site not responding. Last check: 2007-10-06)
		The Conner-Floyd theorem was later generalized by Landweber in his exact functor theorem [Lan].
		3: The structure of the Spin cobordism ring (context) - Anderson, Brown et al.
		6 The structure of the Spin cobordism ring (context) - Anderson, Brown et al.
	citeseer.ist.psu.edu /hopkins95spin.html (519 words)

	Publications of Douglas C. Ravenel (Site not responding. Last check: 2007-10-06)
		Complex cobordism and its applications to homotopy theory, Proceedings of the International Congress of Mathematicians, Helsinki, 1978, 491-496.
		The 7-connected cobordism ring at p=3 (with M. Hovey), Transactions of the Amer.
		The method of infinite descent in stable homotopy theory II (with H.~Nakai), in preparation.
	www.math.rochester.edu /people/faculty/drav/publist.html (1080 words)

	[No title] (Site not responding. Last check: 2007-10-06)
		Abstract: The cobordism theory of smooth high-dimensional sphere knots was completely solved (or at least turned into an algebraic problem) in the 1960s through the work of Kervaire, who showed that all even-dimensional knots are cobordant, and J. Levine, who showed that the cobordism type of an odd-dimensional knot is determined by its Seifert matrix.
		Following a brief review of this material, we introduce disk knots and study their cobordism properties.
		We further study these invariants, obtaining results on the relations between algebraic invariants of disk knots and those of their boundary sphere knots.
	www.wesleyan.edu /cgi-bin/cdf_manager/template_renderer.cgi?item=13574 (140 words)

	[No title]
		Here we extend their programme by discussing the geometric and homotopy theoretical interpretations of the quantum double of the Landweber-Novikov algebra, as represented by a subalgebra of operations in double complex cobordism.
		We base our study on certain families of bounded flag manifolds with double complex structure, originally introduced into cobordism theory by the second author.
		We give background information on double complex cobordism, and discuss the cell structure of the flag manifolds by analogy with the classic Schubert decomposition, allowing us to describe their complex oriented cohomological properties (already implicit in the Schubert calculus of Bressler and Evens).
	claude.math.wesleyan.edu /~mhovey/archive/letter33 (782 words)

	Topology Seminar at UCR (Site not responding. Last check: 2007-10-06)
		After an introductory discussion of knots S^n\subset S^{n+2} and knot cobordism I would like to talk about certain generalizations, boundary link cobordism and F-link cobordism.
		The F_mu-link cobordism group C_n(F_mu) is known to be trivial when n is even but not finitely generated when n is odd.
		The main result I would like to present is an algorithm to decide whether two odd-dimensional F_\mu-links represent the same cobordism class in C_{2q-1}(F_\mu) assuming q>1.
	math.ucr.edu /~xl/TopologySeminar_Fall_2001.html (485 words)

	Adams, J. F.: Stable Homotopy and Generalised Homology
		Frank Adams, the founder of stable homotopy theory, gave a lecture series at the University of Chicago in 1967, 1970, and 1971, the well-written notes of which are published in this classic in algebraic topology.
		The three series focused on Novikov's work on operations in complex cobordism, Quillen's work on formal groups and complex cobordism, and stable homotopy and generalized homology.
		His exposition on the third topic occupies the bulk of the book and gives his definitive treatment of the Adams spectral sequence along with many detailed examples and calculations in KU-theory that help give a feel for the subject.
	www.press.uchicago.edu /cgi-bin/hfs.cgi/00/10.ctl (210 words)

	Algebraic cobordism of simply connected Lie groups, by N. Yagita (Site not responding. Last check: 2007-10-06)
		Let G be a simply connected Lie group and G_C the corresponding algebraic group over the complex number field.
		On the otherhand Levine and Morel recently defined the algebraic cobordism \Omega^(X) such that \Omega^(pt)=\Omega^=MU^ ; the complex cobordism ring, and that \Omega^(X)/\Omega^- = CH^(X) for a smooth algebraic variety X over k of ch(k)=0.
		In this paper we show that the cobordism version of the Grothendieck and Kac holds with modulo I^2, namely, \Omega^(G_C)/I^2=\pi^(MU^*(G/T))/I^2, and compute it explicitely
	www.math.uiuc.edu /K-theory/0518 (143 words)

	Homotopy Groups, Thom Spaces, and the Oriented Cobordism Ring (Site not responding. Last check: 2007-10-06)
		Homotopy Groups, Thom Spaces, and the Oriented Cobordism Ring
		John Baldwin will give the talk on Monday, October 25 at 4:15 in Math 528.
		Furthermore, we can form the oriented cobordism ring, O
	www.math.columbia.edu /~welji/seminar/102504.html (162 words)

	Atlas: The even cobordism category by Patrick M. Gilmer (Site not responding. Last check: 2007-10-06)
		KNOTS in Poland 2003: The mini-semester on Knot Theory and its Ramifications
		We will consider the cobordism category, C, whose objects are closed oriented surfaces equipped with the extra structure of a Langrangian subspace of the rational first homology of the surface, and whose morphisms are 3-dimensional cobordisms equipped with the extra structure of an integer weight.
		The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # calg-44.
	atlas-conferences.com /cgi-bin/abstract/calg-44 (154 words)

	Best Book Buys - Cobordism theory Books (Site not responding. Last check: 2007-10-06)
		Books > Browse > Subject Category > Mathematics > Algebra / General > Cobordism theory
		Subject Category > Mathematics > Algebra / General > Cobordism theory
		Classifying Spaces for Surgery and Cobordism of Manifolds
	www.bestwebbuys.com /General_Algebra-N_10020431-books.html (81 words)

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