Last edited by Voodoolar
Friday, May 8, 2020 | History

4 edition of Künneth theorem and the universal coefficient theorem for equivariant K-theory and KK-theory found in the catalog.

# Künneth theorem and the universal coefficient theorem for equivariant K-theory and KK-theory

## by Rosenberg, J.

• 320 Want to read
• 18 Currently reading

Published by American Mathematical Society in Providence, R.I., USA .
Written in English

Subjects:
• K-theory.,
• KK-theory.,
• Spectral sequences (Mathematics),
• Algebra, Homological.

• Edition Notes

Classifications The Physical Object Other titles Universal coefficient theorem for equivariant K-theory and KK-theory. Statement Jonathan Rosenberg and Claude Schochet. Series Memoirs of the American Mathematical Society,, no. 348 Contributions Schochet, Claude, 1944- LC Classifications QA3 .A57 no. 348, QA612.33 .A57 no. 348 Pagination v, 95 p. ; Number of Pages 95 Open Library OL2717757M ISBN 10 0821823493 LC Control Number 86010959

On the K-Theory Proof of the Index Theorem NIGEL HIGSON 1. Introduction This paper is an exposition of the K-theory proof of the Atiyah-Singer Index Theorem. I have tried to separate, as much as possible, the analytic parts of the proof from the topological calculations. For the topology I have taken advantage. Universal Coeﬃcient Theorem for Cohomology We present a direct proof of the universal coeﬃcient theorem for cohomol-ogy. It is essentially dual to the proof for homology. Theorem 1 Given a chain complex C in which each C n is free abelian, and a coeﬃcient group G, we have for each n the natural short exact sequence 0 −−→ Ext(HFile Size: 86KB.

Algebraic K-Theory plays an important role in many areas of modern mathematics: most notably algebraic topology, number theory, and algebraic geometry, but even including operator theory. The broad range of these topics has tended to give the subject an aura of inapproachability. This book, based on a course at the University of Maryland in the fall of , is intended to enable graduate. In mathematics, the equivariant 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.

SOME REMARKS ON THE UNIVERSAL COEFFICIENT THEOREM IN KK-THEORY 5 Passing to the inductive limit we obtain an exact sequence (3) 0!SF ›K! A0!U! 0 where U is the universal UHF algebra. From (3) and Proposition we see that A satisﬁes the UCT if and only if F does so. ⁄ Using the extension (3) and its construction we see that K⁄(A)»= K⁄(A0)»= K⁄(SA) 'File Size: KB. This fact is mentioned and used in Roberto Frigerio's book "Bounded cohomology of discrete groups", and referred to as the Universal Coefficient theorem. However, all the references I could find for the Universal Coefficient Theorem in cohomology are either in the algebraic topology setting, or in a general homological algebra setting, but with.

Available for Download

Share this book
You might also like
The works of the ever memorable Mr. John Hales of Eaton

The works of the ever memorable Mr. John Hales of Eaton

A slim queen in a palanquin

A slim queen in a palanquin

William Dawson Armstrong

William Dawson Armstrong

From Serajevo to the Rhine

From Serajevo to the Rhine

Soil survey of Newton County, Arkansas

Soil survey of Newton County, Arkansas

Dunciad

Dunciad

Weld quality control and inspection.

Weld quality control and inspection.

Records and songs of Saxon times

Records and songs of Saxon times

Engineering thermodynamics

Engineering thermodynamics

Report on results of discussions with industry on the second programme targets.

Report on results of discussions with industry on the second programme targets.

Comparative and cellular pathophysiology of epilepsy.

Comparative and cellular pathophysiology of epilepsy.

Graduate education for hospital administration in the United States: trends

Graduate education for hospital administration in the United States: trends

Elements of international law.

Elements of international law.

A method of quantitative analysis of trace elements in silicate rocks by energy-dispersive X-ray fluorescence spectroscopy

A method of quantitative analysis of trace elements in silicate rocks by energy-dispersive X-ray fluorescence spectroscopy

Family matters

Family matters

### Künneth theorem and the universal coefficient theorem for equivariant K-theory and KK-theory by Rosenberg, J. Download PDF EPUB FB2

The Kunneth Theorem and the Universal Coefficient Theorem for Equivariant K-Theory and Kk-Theory (Memoirs of the American Mathematical Society) UK ed. Edition by J. Rosenberg (Author) › Visit Amazon's J. Rosenberg Page. Find all the books, read about the author, and more. Cited by:   The Kunneth Theorem and the Universal Coefficient Theorem for Equivariant $K$-Theory and $KK$-Theory.

Memoirs of the American Mathematical Society. ; 95 pp; MSC: Primary 46; Secondary 18; 19; Electronic ISBN:. Atiyah-Singer equivariant index theorem for families.

Note that the usual equivariant K-theory groups arise via the identification K^(B) 2 KKj(for equivariant K-theory and KK-theory. Get this from a library. The Künneth theorem and the universal coefficient theorem for equivariant K-theory and KK-theory. [Jonathan M Rosenberg; Claude Schochet] -- For any pair ([italic]A, [italic]B) of [italic]C*-algebras equipped with continuous actions of a locally compact group [italic]G, denote by [italic]KK[italic exponent]G [over] [subscript]*.

Künneth theorem and the universal coefficient theorem for equivariant K-theory and KK-theory / Material Type: Document, Internet resource: Document Type: Internet Resource, Computer File: All Authors / Contributors: Jonathan M Rosenberg; Claude Schochet.

It follows that if A and B are unital separable nuclear purely infinite simple C*-algebras which satisfy the Universal Coefficient Theorem, and if there is a graded isomorphism from K_* (A) to K.

Abstract: For T an abelian compact Lie group, we give a description of T-equivariant K-theory with complex coefficients in terms of equivariant cohomology. In the appendix we give applications of this by extending results of Chang-Skjelbred and Goresky-Kottwitz-MacPherson from equivariant cohomology to equivariant : Ioanid Rosu, Allen Knutson.

An introduction to the Universal Coe cient Theorem S˝ren Eilers and we establish a Universal Coefficient Theorem (UCT) of the form 0 Ext(K,(A), K,(B)) KK,(A, B etc.) in topological K-theory.

For reasons to be explained later, our UCT also determines this product structure. In particular, we determine the structure of the graded ring KK. In algebraic topology, universal coefficient theorems establish relationships between homology and cohomology theories.

For instance, the integral homology theory of a topological space X, and its homology with coefficients in any abelian group A are related as follows: the integral homology groups H i (X; Z) completely determine the groups H i (X; A).

G(X), the category of G-equivariant vector bundles on a topological space X. K(Vect G(X)) is known as equivariant (topological) K-theory. • C = Coh(X), the category of coherent sheaves on an algebraic variety X.

This is called algebraic K-theory If we wish to generalize this last example to the equivariant setting, we have to beFile Size: KB. from book Topics in algebraic and topological K-theory.

Papers based on the Sedano winter school on K-theory (Swisk), Sedano, Spain, January 22–27, (pp) Universal Coefficient.

$\begingroup$ This is not a meaningful question, because the isomorphism (2) is not canonical, not natural, not well-defined. The map that you call $\pi_1$ is natural, but the careful statement of the universal coeff thm says only that that map is split surjective and that its.

For KK-theory. Discussion for KK-theory is in. Jonathan Rosenberg, Claude Schochet, The Künneth theorem and the universal coefficient theorem for Kasparov’s generalized K-functor, Duke Math. Vol Number 2 (), The Künneth theorem and the universal coefficient theorem for Kasparov’s generalized K-functor.

Duke Math. 55 (2), – () MR (88i) Google Scholar Cited by: 2. The Künneth theorem and the universal coefficient theorem for Kasparov’s generalized K-functor Jonathan Rosenberg and Claude Schochet More by Jonathan Rosenberg.

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 Abstract: In this paper, we study the algebraic analogue of the topological Atiyah-Segal completion theorem. We verify this completion theorem for the algebraic.

EquivariantKK-theory and the Novikov conjecture. The Künneth theorem and the universal coefficient theorem for Kasparov's generalizedK-functor. Duke Math. J, – () Google Scholar [Sa] Sakai, S.:C *-algebras andW *-algebras.

New York Heidelberg Berlin: Springer G.G. EquivariantKK-theory and the Novikov conjecture Cited by: Lectures on Algebraic K theory by J.F. Jardine. This note covers the following topics: Some homotopy theory, Exact categories, Q-construction, Fundamental groupoid, Waldhausen's constructions, Additivity, The K-theory spectrum, Products, Group completion, Q=+ theorem, The defining acyclic map, Homotopy fibres, Resolution theorem, Dévissage, Abelian category localization, Coherent sheaves and.

Topics in K-Theory The Equivariant Künneth Theorem in K-Theory. Dyer-Lashof operations in K-Theory. Authors: Hodgkin, L.H., Snaith, V.P. Free Preview. It will be a consequence of this theorem and a result of Milnor that the inverse limit of K G(X EG n) ˘=K G(X EG).

Since equivariant K-theory on a space with free G-action is the same as the K-theory of the quotient, we have the following consequence of the completion theorem: Corollary If Kq G (X) is nitely generated as a module over R(G.so we need a theorem which will establish the relationship between homology of arbitrary coe cients and homology with Z coe cients.

In Section 2, we will give the necessary algebra background. In Section 3 we will de ne Tor and prove the Universal Coe cient Theorem for Homology.

In the last section, we will compute two examples. 2 Background in.to a stable (∞, 1) (\infty,1)-category which is universal with the property that it respects colimits and exact sequences in a suitable any stable (∞, 1) (\infty,1)-category A A, its (connective or non-connective, depending on details) algebraic K-theory spectrum is the hom-object.