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Sunday, May 17, 2020 | History

3 edition of Equivariant cobordism and K-theory found in the catalog.

Equivariant cobordism and K-theory

Steven R. Costenoble

Equivariant cobordism and K-theory

by Steven R. Costenoble

  • 135 Want to read
  • 17 Currently reading

Published .
Written in English


Edition Notes

Statementby Steven R. Costenoble.
Classifications
LC ClassificationsMicrofilm 85/4537 (Q)
The Physical Object
FormatMicroform
Pagination82 leaves.
Number of Pages82
ID Numbers
Open LibraryOL2691185M
LC Control Number85892938

$\begingroup$ I guess a better question would be something like "is it in fact known for some general classes of (X, G) that the image via these two maps recovers equivariant K-theory?" References for where statements like this are proved is what I was asking for I guess $\endgroup$ – A. S. May 17 '18 at 8: Equivariant elliptic cohomology and K-theory Constantin Teleman 1. Background Elliptic cohomology Ellis a functor assigning to every elliptic curve a complex-oriented cohomology theory, namely the theory based on the formal group law of that curve. Away from the prime 2, theFile Size: KB.

References [1] D. W. Anderson, Thesis, Berkeley, [2] M. F. Atiyah and F. Hirzebruch, Vector bundles and homogeneous spaces, Proc. Sympos. Pure Math. Vol. 3 Cited by: equivariant K-theory of algebraic groups: Corollary Let H be a closed subgroup of an algeraic group G. Then G is an H-scheme by left translations and there is a natural isomorphism p∗: K 0 n (G/H) →∼ K n (H;G). Basic results in equivariant K-theory. We formulate basic state-ments in the equivariant algebraic K-theory developed.

Equivariant and motivic homotopy theory Reed College, May , Performing Arts Building Contact Kyle Ormsby or Angélica Osorno with questions. Ivo Dell'Ambrogio, Heath Emerson, Tamaz Kandelaki, Ralf Meyer, A functorial equivariant K-theory spectrum and an equivariant Lefschetz formula (arXiv) This article in turn considers a variant of the construction in (Bunke-Joachim-Stolz 03) which gives operator K-theory spectra that are functorial for general * \ast-homomorphisms.


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Equivariant cobordism and K-theory by Steven R. Costenoble Download PDF EPUB FB2

Equivariant Chern-character. There is a Chern character map from equivariant K-theory to equivariant ordinary cohomology. (e.g. Stefanich) Related concepts. Baum-Connes conjecture, Green-Julg theorem.

Atiyah-Segal completion theorem. equivariant elliptic cohomology. representation rings and topological equivariant K-theory in section 5. As we discuss briefly in section 7, this result and the equivariant Dold theorem mod k of Hauschild and Waner [13] can be used to prove the following equivariant version of the Adams conjecture.

Theorem Topology Vol. ;86 $ Printed in Great Britain. r Pergamon Press Ltd. GEOMETRIC EQUIVARIANT BORDISM AND K-THEORY IMADSEN (Received I June ) THIS paper studies the relationship between equivariant bordism and equivariant K-theory, generalizing a celebrated result of Conner and Floyd to the equivariant Cited by: 9.

The goal of these lectures is to give an introduction to equivariant algebraic K-theory. Out motivation will be to provide a proof of the classical Weyl character formula using a localization result.

Our primary reference is the book of Chriss-Ginzburg [1], chapters 5 File Size: KB. For the topological equivariant K-theory, see topological K-theory. In mathematics, the Equivariant cobordism and K-theory book algebraic K-theory is an algebraic K-theory associated to the category ⁡ of equivariant coherent sheaves on an algebraic scheme X with action of a linear algebraic group G, via Quillen's Q-construction; thus, by definition, = (+ ⁡ ()).In particular, () is the Grothendieck.

Analogues of this description hold for other complex-oriented equivariant cohomology theories, as we confirm in the case of homotopical complex cobordism, which is the universal by: 2. equivariant topological K-theory, an equivariant analog of topological K-theory Disambiguation page providing links to topics that could be referred to by the same search term This disambiguation page lists articles associated with the title Equivariant K-theory.

Cobordism invariance for families is then a consequence of the functoriality of the index map and, moreover, it depends only on properties of the symbol K-theory class of a given elliptic family. Introduces equivariant homotopy, homology, and cohomology theory, along with various related topics in modern algebraic topology.

This book begins with a development of the equivariant algebraic Read more. Equivariant Cobordism for Torus Actions. Book. Jan ; We finally discuss the equivariant K-theory of these varieties with finite coefficients and prove the equivariant version of the Author: Amalendu Krishna.

The purpose of this book is to present research generalizing equivariant K-theory for actions of compact groups to the case of proper actions of locally compact groups. Under the technically convenient assumption that everything is second countable, the basic properties of equivariant K-theory for proper actions are by: I of the spectrum KG that represents equivariant K-theory.

We shall explain a still more recent result which states that a similar analysis works to give the same kind of localization and completion theorems for the spectrum MUG that represents a stabilized version of equivariant complex cobordism and for all module spectra over MUG. We shall.

Cobordism theory became part of the apparatus of extraordinary cohomology theory, alongside K-theory. It performed an important role, historically speaking, in developments in topology in the s and early s, in particular in the Hirzebruch–Riemann–Roch theorem, and in the first proofs of the Atiyah–Singer index theorem.

4. Equivariant K-theory spectra ; 5. The Atiyah-Segal completion theorem ; 6. The generalization to families ; Chapter XV. An introduction to equivariant cobordism ; 1. A review of nonequivariant cobordism ; 2. Equivariant cobordism and Thorn spectra ; 3.

Computations: the use of families ; 4. The first third of this book is a detailed exposition of equivariant K-theory and KK-theory, assuming only a general knowledge of C*-algebras and some ordinary K-theory.

It continues with the author's research on K-theoretic freeness of : Perfect Paperback. My talk The coefficients of stable equivariant cobordism for a finite abelian group on joint work with Will Abram. Winter School of Geometry and Physics, Srni Lecture notes of joint lectures of Po Hu and Igor Kriz on Equivariant and non-equivariant homotopy theory: Lecture 1 Lecture 2 Lecture 3 Lecture 4.

Equivariant K-theory 3 Introduction Theequivariant K-theory was developed by on in[21].Let analgebraic groupG actonavariety X iderG-modules,i.e.,O X-modules over X that are equipped with an G-action compatible with one on e non-equivariant case there are two categories: the abelian category M(G;X) ofcoherent G-modules File Size: KB.

An equivariant surgery sequence and equivariant diffeomorphism and homeomorphism classification (announcement). Topology Symposium Siegen (Lect. Notes Math. vol.pp. –) Berlin Heidelberg New York: Springer Google ScholarCited by: The homotopy limit problem for Karoubiʼs Hermitian K-theory (Karoubi, ) was posed by Thomason ().There is a canonical map from algebraic Hermitian K-theory to the Z / 2-homotopy fixed points of algebraic problem asks, roughly, how close this map is to being an isomorphism, specifically after completion at by: Submission history From: Mona Merling [] Thu, 28 May GMT (55kb) Thu, 9 Jul GMT (57kb) [v3] Mon, 12 Sep GMT (51kb)Cited by: 1.

To send this article to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon by: of Kasparov’s equivariant KK-theory [23] for calculating the K-theory of group C∗-algebras.

A central problem in C∗-algebra K-theory is the Baum-Connes con-jecture [4], which proposes a formula for the K-theory of group C∗-algebras. A primary goal of the paper is to first formulate the conjecture in the language of.Search within book.

Front Matter. The Thom isomorphism in K-theory. P. E. Conner, E. E. Floyd. Pages Cobordism characteristic classes.

P. E. Conner, E. E. Floyd. Pages U-manifolds with framed boundaries About this book. Keywords. Characteristic class K-Theorie K-theory Kobordismus Manifold Morphism Relation Topologie.