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Thursday, August 13, 2020 | History

4 edition of Algebraic cobordism and K-theory found in the catalog.

Algebraic cobordism and K-theory

V. P. Snaith

Algebraic cobordism and K-theory

by V. P. Snaith

  • 9 Want to read
  • 20 Currently reading

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

    Subjects:
  • Cobordism theory.,
  • K-theory.,
  • Homotopy theory.

  • Edition Notes

    StatementVictor P. Snaith.
    SeriesMemoirs of the American Mathematical Society ; no. 221, Memoirs of the American Mathematical Society ;, no. 221.
    Classifications
    LC ClassificationsQA3 .A57 no. 221, QA612.3 .A57 no. 221
    The Physical Object
    Paginationvii, 152 p. ;
    Number of Pages152
    ID Numbers
    Open LibraryOL4414195M
    ISBN 100821822217
    LC Control Number79017981

    Atiyah's works on K-theory, including his book on K-theory are reprinted in volume 2 of his collected works. [40] The simplest nontrivial example of a vector bundle is the Möbius band (pictured on the right): a strip of paper with a twist in it, which represents a rank 1 vector bundle over a circle (the circle in question being the centerline. Algebraic cobordism and K-theory by Victor P Snaith (Book) 16 editions published between and in 4 languages and held by WorldCat member libraries worldwide.

    The S_dot construction and Waldhausen's algebraic K-theory of spaces A(*) is K(S) References: Rognes' notes on the stable parametrized h-cobordism theorem; Waldhausen: “Algebraic K-theory of Spaces” (SLNM ) Waldhausen: “An outline of how manifolds relate to algebraic K-theory”. Algebraic cobordism and K-theory 92 Projective bundles 92 Universal property of K-theory 96 The cobordism ring of a point The canonical splitting The main theorem Birational invariant theories Degree formulas The degree homomorphism

    cobordism, it became possible to de ne an equivalent tool for the language of schemes. Levine and Moore [35] translated Quillen’s axioms into algebraic geometry and de ned algebraic cobordism. This theory has strong relations with the Chow group and K-theory, just like cobordism theories. Lectures on the H-Cobordism Theorem by John Milnor,, available at Book Depository with free delivery worldwide. Lectures on the H-Cobordism Theorem: John Milnor: We use cookies to give you the best possible experience.5/5(1). 1 Introduction. The theory of bordism is one of the deepest and most influential parts of algebraic topology.


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Algebraic cobordism and K-theory by V. P. Snaith Download PDF EPUB FB2

Readers of this book will have to bring with them a solid understanding of algebraic geometry at the level of the theory of schemes, and an in-depth knowledge of classical cobordism theory as is found in the works of the mathematician Daniel Quillen or the book by Robert by:   Algebraic K-theory is a subject area in mathematics with connections to geometry, topology, ring theory, and number ric, algebraic, and arithmetic objects are assigned objects called are groups in the sense of abstract contain detailed information about the original object but are notoriously difficult to compute; for example, an important.

Get this from a library. Algebraic cobordism and K-theory. [Victor P Snaith] -- A decomposition is given of the S-type of the classifying spaces of the classical groups. This decomposition is in terms of Thom spaces and by means of it cobordism groups are embedded into the.

They prove the existence of a universal such theory (in characteristic 0) called Algebraic Cobordism. Surprisingly, this theory satisfies the analogues of Quillen's theorems: the cobordism of the base field is the Lazard ring and the cobordism of a smooth variety is generated over the Lazard ring by the elements of positive degrees.

Chapter IV. Algebraic cobordism and the Lazard ring 67 Weak homology and Chern classes 67 Algebraic cobordism and K-theory 85 The cobordism ring of a point 94 Degree formulas 99 Comparison with the Chow groups Chapter V. Oriented Borel-Moore homology Oriented Borel-Moore homology theories Other.

Algebraic Cobordism (Springer Monographs in Mathematics) - Kindle edition by Levine, Marc, Morel, Algebraic cobordism and K-theory book. Download it once and read it on your Kindle device, PC, phones or tablets.

Use features like bookmarks, note taking and highlighting while reading Algebraic Cobordism (Springer Monographs in Mathematics).Reviews: 1. For many years, algebraic topology rests on three legs: "ordinary" cohomology, K-theory, and cobordism.

This book is the first guide on the subject of cobordism since R. Stong's encyclopaedic and influential notes of a generation ago. It concentrates on Thom spaces (spectra), orientability theory and (co)bordism theory (including (co)bordism.

Buy Algebraic Cobordism (Springer Monographs in Mathematics) by Marc Levine, Fabien Morel (ISBN: ) from Amazon's Book Store. Everyday low. Dominique Arlettaz, Algebraic K-theory of rings from a topological viewpoint.

Daniel Grayson, Quillen’s work in algebraic K-theory, J. K-Theory 11 (), – pdf. An introductory textbook account is in. Charles Weibel, The K-Book: An introduction to algebraic K-theory. The term ‘algebraic L-theory’ was coined by Wall, to mean the algebraic K-theory of quadratic forms, alias hermitian K-theory.

In the classical theory of quadratic forms the ground ring is a eld, or a ring of integers in an algebraic number eld, and quadratic forms are classi ed up to isomorphism. Bordism and cobordism theories 34 Further work on cobordism and its relation to K-theory 37 High dimensional geometric topology 40 Iterated loop space theory 42 Algebraic K-theory and homotopical algebra 43 The stable homotopy category 45 References 50 Stable algebraic topology is one of the most theoretically deep and.

Based on the algebraic cobordism theory of Levine and Morel, we develop a theory of algebraic cobordism modulo algebraic equivalence. We prove that this theory can reproduce Chow groups modulo algebraic equivalence and the semi-topological K also show that with finite coefficients, this theory agrees with the algebraic cobordism theory.

Algebraic K-theory, which is the main character of this book, deals mainly with studying the structure of rings. However, it turns out that even working in a purely algebraic context, one requires techniques from homotopy theory to construct the higher K-groups and to perform computations. The resulting interplay of algebra, geometry, and.

In mathematics, algebraic cobordism is an analogue of complex cobordism for smooth quasi-projective schemes over a was introduced by Marc Levine and Fabien Morel (, b). An oriented cohomology theory on the category of smooth quasi-projective schemes Sm over a field k consists of a contravariant functor A* from Sm to commutative graded rings, together with push-forward maps f.

Browse other questions tagged aic-topology cohomology kt.k-theory-and-homology cobordism or ask your own question. The Overflow Blog The Loop, August Community-a-thon. Algebraic cobordism The Conner-Floyd theorem We recover both K 0 and CH from.

Theorem The canonical map alg 0!K [ ; 1] is an isomorphism, i.e., Kalg 0 [ ; 1] is the universal multiplicative theory over k. Theorem The canonical map +!CH is an isomorphism, i.e., CH is the universal additive theory over k.

Marc Levine Algebraic Cobordism. Readers of this book will have to bring with them a solid understanding of algebraic geometry at the level of the theory of schemes, and an in-depth knowledge of classical cobordism theory as is found in the works of the mathematician Daniel Quillen or the book by Robert Stong.

``The K-book: an introduction to algebraic K-theory'' by Charles Weibel (Graduate Studies in Math. vol. AMS, ) Errata to the published version of the K-book.

Note: the page numbers below are for the individual chapters, and differ from the page numbers in the published version of the K-book. The Theorem/Definition/Exercise numbers are.

These are all framed by (co)homology theories and spectra. The book is easy to use by students, for when proofs are not given, specific references are. MathSciNet gives an enthousiastic review, "The book is indispensable for research workers in algebraic topology. The presentation of the material is very nice and thorough, and this makes the.

Weak homology and Chern classes -- Algebraic cobordism and K-theory -- The cobordism ring of a point -- Degree formulas -- Comparison with the Chow groups -- V. Oriented Borel-Moore homology -- This implies in particular the generalized degree formula conjectured by Rost.

The book also contains some examples of. BIBLIOGRAPHY Araki, S. [1] Typical formal groups in complex cobordism and K-theory, Kinokuniya Book-Store Co. Ltd., Tokyo, Aubry, M. [1] Calculs de groupes d’homotopie stables de la sph ere, par la suite spectrale d’Adams{Novikov.that algebraic K-theory defines a presheaf of (ordinary) E∞ spectra on an appropriate site.

This is already known to be the case for algebraic cobordism, where it is clear from the construction of MGL, but does not appear to be known either for periodic algebraic cobordism or algebraic K-theory.

Documenta Mathematica 14 () –Coefficient ring: π * (BP) is a polynomial algebra over Z (p) on generators v n of dimension 2(p n − 1) for n ≥ 1. Brown–Peterson cohomology BP is a summand of MU p, which is complex cobordism MU localized at a prime p.

In fact MU (p) is a sum of suspensions of BP. Morava K-theory. Spectrum: K(n) (They also depend on a prime p.).