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Monday, August 10, 2020 | History

5 edition of Operations in connective K-theory found in the catalog.

Operations in connective K-theory

by Richard M. Kane

  • 320 Want to read
  • 31 Currently reading

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

    Subjects:
  • K-theory.,
  • Steenrod algebra.,
  • Homotopy groups.

  • Edition Notes

    StatementRichard M. Kane.
    SeriesMemoirs of the American Mathematical Society,, no. 254
    Classifications
    LC ClassificationsQA3 .A57 no. 254, QA612.33 .A57 no. 254
    The Physical Object
    Paginationvi, 102 p. ;
    Number of Pages102
    ID Numbers
    Open LibraryOL4268826M
    ISBN 100821822543
    LC Control Number81014883

    This handbook offers a compilation of techniques and results in K-theory. These two volumes consist of chapters, each of which is dedicated to a specific topic and is written by a leading expert. Many chapters present historical background; some present previously unpublished results, whereas some. Buy Connective Real K-Theory of Finite Groups by Robert R. Bruner, J.P.C. Greenlees from Waterstones today! Click and Collect from your local Waterstones .

    Real and complex K-theory. The set of isomorphism classes of real vector bundles over a nite CW complex Xforms a commutative monoid with respect to direct (Whitney) sum of vector bundles. There are connective, i.e. (1)-connected, covers of these ring spectra, denotes koand ku, respectively. More precisely, ku∗(X) is the cohomology represented by the connective cover of the spectrum K representing Atiyah-Hirzebruch periodic complex K theory. Their values on a point are K∗= Z[v,v−1] and ku∗= Z[v], where vis the Bott periodicity element in degree 2. Connective K theory is relatively easy to calculate, and it has been used to.

    Prominent examples include stable homotopy, K-theory or bordism. Global equivariant homotopy theory studies such uniform phenomena, i.e. universal symmetries encoded by simultaneous and compatible actions of all compact Lie groups. This book introduces graduate students and researchers to global equivariant homotopy theory. According to a preprint by Nobuaki Yagita, the conjecture on a relationship between K - and Chow theories for a generically twisted flag variety of a split semisimple algebraic group G, due to the author, fails for G the spinor group Spin (1 7).Yagita’s tools include a Brown–Peterson version of algebraic cobordism, ordinary and connective Morava K-theories, as well as Grothendieck.


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Operations in connective K-theory by Richard M. Kane Download PDF EPUB FB2

Get this from a library. Operations in connective K-theory. [Richard M Kane] -- This paper constructs and studies a family {[italic]Q[italic]n} of operations in complex connective K-theory.

The operations arise from splitting [italic]b[italic]u [wedge product. Electronic books: Additional Physical Format: Print version: Kane, Richard M., Operations in connective K-theory / Material Type: Document, Internet resource: Document Type: Internet Resource, Computer File: All Authors / Contributors: Richard M Kane.

Title (HTML): Operations in Connective \(K\)-Theory Author(s) (Product display): Richard M. Kane Book Series Name: Memoirs of the American Mathematical Society.

In p-local connective K-theory, the degree zero operations k (p) 0 (k (p)) form a bicommutative bialgebra, which we denote by k 0 (k) (p). Note, however that this is not the p-localisation of the bialgebra k 0 (k) of integral operations, but is isomorphic to the completed tensor product k 0 (k) ⊗ ^ Cited by: In this article we classify additive operations in connective K-theory with various torsion-free coefficients.

We discover that the answer for the integral case requires understanding of the. ADAMS OPERATIONS IN THE CONNECTIVE K-THEORY OF COMPACT LIE GROUPS TAKASHI WATANABE (Received ) 1.

Introduction Let G be a compact, 1-connected, simple Lie group of rank 2 or 3. That is, G is one of the following: SU(3): Sp(2), G 2, SU(4), Operations in connective K-theory book and Sρ(3). In [14], for these groups G, we have given a complete description of the.

It was scary, because (in ) I didn't know even how to write a book. I needed a warm-up exercise, a practice book if you will. The result, An introduction to homological algebra, took over five years to write.

By this time (), the K-theory landscape had changed, and with it my vision of what my K-theory book should be. Was it an obsolete. a group of p-adic infinite upper triangular matrices and certain operations fo r the Adams summand of com plex connective K -theory. Let ku be the p -adic connective complex K -theory.

References. A standard textbook account is in section 2 of. Bruce Blackadar, K-Theory for Operator Algebras (); Other introductions include. Rørdam, F. Larsen, N. Laustsen, An introduction to K-theory for C * C^\ast-algebras, London Mathematical Society Student Textx.

By this time (), the K-theory landscape had changed, and with it my vision of what my K-theory book should be. Was it an obsolete idea.

After all, the new developments in Motivic Cohomology were affecting our knowledge of the K-theory of fields and varieties. In addition, there was no easily accessible source for this new material.

Download PDF Abstract: In this article we classify additive operations in connective K-theory with various torsion-free coefficients. We discover that the answer for the integral case requires understanding of the $\widehat{\mathbb{Z}}$ one. Moreover, although integral additive operations are topologically generated by Adams operations, these are not reduced to infinite linear combinations of.

Higher genera for proper actions of Lie groups Piazza, Paolo and Posthuma, Hessel B., Annals of K-Theory, Representation types and 2-primary homotopy groups of certain compact Lie groups Davis, Donald M., Homology, Homotopy and Applications, This paper is devoted to the connective K homology and cohomology of finite groups G.

We attempt to give a systematic account from several points of view. In Chapter 1, following Quillen [50, 51], we use the methods of algebraic geometry to study the ring ku*(BG) where ku denotes connective complex K-theory.

The object of this chapter is to establish the basic result which relates the upper triangular group to operations in connective K-theory. This result will identify a certain group of operations with the infinite upper triangular group with entries in the 2-adic integers. This identification will be canonical up to inner automorphisms.

As a particular application of algebraic K-theory, let me mention the intersection product on regular schemes. Let X be a regular scheme over spec Z. Then, one can use the Quillen spectral sequence and Adam's operations on K-theory to produce an intersection product on the Chow groups tensored with Q.

Periodic K-theory and maps into classical fibrations 36 Near the edge of periodicity 41 Chapter 3. Descent, Twisting and Periodicity 49 Fixed points, homotopy fixed points and geometric fixed points 49 Descent 50 Statement of periodicity for equivariant connective real K-theory 52 Periodicity for connective real.

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Lectures On K theory. This book covers the following topics: Topological K-Theory, Topological Preliminaries on Vector Bundles, Homotopy, Bott Periodicity and Cohomological Properties, Chern Character and Chern Classes, Analytic K-Theory, Applications of Adams operations, Higher Algebraic K-Theory, Algebraic Preliminaries and the the.

logical filtration in algebraic K-theory. As a result, we obtain a construction of the first Steenrod square for Chow groups modulo two of varieties over a field of arbitrary characteristic. This improves previously obtained results, in the sense that it is not anymore needed to mod out the image modulo two of.

Let X be a smooth algebraic variety over an arbitrary field. Let φ be the canonical surjective homomorphism of the Chow ring of X onto the ring associated with the Chow filtration on the Grothendieck ring K (X).We remark that φ is injective if and only if the connective K-theory CK (X) coincides with the terms of the Chow filtration on K (X).As a consequence, CK (X) turns out to be.

Upper triangular matrices and operations in odd primary connective K -theory Upper triangular matrices and operations in odd primary connective K -theory Stanley, Laura; Whitehouse, Sarah Abstract We prove analogues for odd primes of results of Snaith and Barker–Snaith.

Let ℓ denote the p -complete connective Adams summand and consider the group of .(2)Non-connective K-theory (3)Universal property (4) K-theory of open immersion of schemes (5)Weibel’s conjecture (6)Co nality theorem and connection to connective K-theory Connections to classical K-theory.

(1)Exact 1-categories (Or Waldhausen, depending on what is easier to connect to the previous) (2) K-theory of exact 1-categories.Upper triangular matrices and operations in odd primary connective K-theory. By Laura Stanley and Sarah Whitehouse.

Abstract. We prove analogues for odd primes of results of Snaith and Barker-Snaith. Let l denote the p-complete connective Adams summand and consider the group of left l-module automorphisms of l smash l in the stable homotopy.