5 edition of Algebraic K-theory and localised stable homotopy theory found in the catalog.
Bibliography: p. 98-102.
|Series||Memoirs of the American Mathematical Society,, no. 280|
|LC Classifications||QA3 .A57 no. 280, QA612.33 .A57 no. 280|
|The Physical Object|
|Pagination||xi, 102 p. ;|
|Number of Pages||102|
|LC Control Number||83003726|
In mathematics, stable homotopy theory is that part of homotopy theory (and thus algebraic topology) concerned with all structure and phenomena that remain after sufficiently many applications of the suspension functor. A founding result was the Freudenthal suspension theorem, which states. Algebraic K-theory is a subject area in mathematics with connections to geometry, topology, ring theory, and number theory. Geometric, algebraic, and arithmetic objects are assigned objects called K-groups. These are groups in the sense of abstract algebra. They contain detailed information about the original object but are notoriously difficult to compute; for example, an important outstanding problem is to compute the K-groups .
Structured Stable Homotopy Theory and the Descent Problem for the Algebraic K-theory of Fields Gunnar Carlsson1 Department of Mathematics Stanford University Stanford, California Contents 1 Introduction 3 2 Preliminaries 11 3 Completions 15 4 Endomorphism algebras for K-theory spectra Algebraic K-theory is a tool from homological algebra that defines a sequence of functors from rings to abelian groups. algebraic-geometry homotopy-theory higher-category-theory algebraic-k-theory stable-homotopy-theory. asked Oct 7 '19 at user algebraic-geometry commutative-algebra homological-algebra algebraic-k-theory.
Algebraic K-Theory and Localised Stable Homotopy Theory. 点击放大图片 出版社: American Mathematical Society. 作者: Snaith, Victor P. 出版时间: 年12月15 日. 10位国际标准书号: 13位国际标准 Algebraic K-Theory and Localised Stable Homotopy Theory. P. Gabriel and M. Zisman, Calculus of fractions and homotopy theory, Ergebnisse der Mathematik und ihrer Grenzgebiete, B Springer (). Google Scholar by:
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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 Cited by: Algebraic K-theory and localised stable homotopy theory.
[Victor P Snaith] -- There is a homomorphism from the stable homotopy of the classifying space of the group of units in a ring to its algebraic [italic]K-theory. Topological K-theory has become an important tool in topology. Using K- theory, Adams and Atiyah were able to give a simple proof that the only spheres which can be provided with H-space structures are S1, S3 and S7.
Moreover, it is possible to derive a substantial part of stable homotopy theory from by: Topological K-theory has become an important tool in K- theory, Adams and Atiyah were able to give a simple proof that the only spheres which can be provided with H-space structures are S1, S3 and er, it is possible to derive a substantial part of stable homotopy theory from K-theory.
Beginning with an introduction to the homotopy theory of simplicial sets and topos theory, the book covers core topics such as the unstable homotopy theory of simplicial presheaves and sheaves, localized theories, cocycles, descent theory, non-abelian cohomology, stacks, and local stable homotopy : Springer-Verlag New York.
Kup książkę Algebraic K-Theory and Localised Stable Homotopy Theory (Victor P. Snaith) u sprzedawcy godnego zaufania.
Przeczytaj fragment, zapoznaj się z opiniami innych czytelników, przejrzyj książki o podobnej tematyce, które wybraliśmy dla Ciebie z naszej milionowej kolekcji. from our sellection of 20 million titles. Algebraic K-Theory I. Proceedings of the Conference Held at the Seattle Research Center of Battelle Memorial Institute, August 28 - September 8, 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 idea. After all, the new developments in Motivic Cohomology were affecting our knowledge of the K-theory of fields and varieties. This unfinished book is intended to be a fairly short introduction to topological K-theory, starting with the necessary background material on vector bundles and including also basic material on characteristic classes.
For further information or to download the part of the book that is written, go to the download page. The most modern and thorough treatment of unstable homotopy theory available. The focus is on those methods from algebraic topology which are needed in the presentation of results, proven by Cohen, Moore, and the author, on the exponents of homotopy : Joseph Neisendorfer.
Using- theory, Adams and Atiyah were able to give a simple proof that the only spheres which can be provided with //-space structures are S^, S^ and S'^.
Moreover, it is possible to derive a substantial part of stable homotopy theory from A^-theory (cf. Adams ). Further applications to analysis and algebra are found in the work of 5/5(2). Stable homotopy of algebraic theories Stefan Schwede Fakulta(tfu(r Mathematik, Universita(t Bielefeld, Bielefeld, Germany Received 1 December ; received in revised form 25 October ; accepted 19 April Abstract The simplicial objects in an algebraic category admit an abstract homotopy theory via a Quillen model categorystructure.
Axiomatic stable homotopy theory About this Title. Mark Hovey, John H. Palmieri and Neil P. Strickland. Publication: Memoirs of the American Mathematical Society Publication Year VolumeNumber ISBNs: (print); (online)Cited by: Book Description: This book contains accounts of talks held at a symposium in honor of John C.
Moore in October at Princeton University, The work includes papers in classical homotopy theory, homological algebra, rational homotopy theory, algebraic K-theory of.
Connective stable homotopy theory 76 8. Semisimple stable homotopy theory 78 9. Examples of stable homotopy categories 80 A general method 80 Chain complexes 82 The derived category of a ring 83 Homotopy categories of equivariant spectra 86 Cochain complexes of B-comodules 89 The stable category of B-modules 95 Cited by: With algebraic K-theory as an intermediary, there has been a growing volume of work that relates algebraic geometry to stable homotopy theory.
With Waldhausen’s introduction of the algebraic K-theory of spaces in the late ’s, stable homotopy became a bridge between algebraic K-theory and the study of diffeomorphisms of manifolds. Algebraic Methods in Unstable Homotopy Theory This is a comprehensive up-to-date treatment of unstable homotopy.
The focus is on those methods from algebraic topology which are needed in the presentation of results, proven by Cohen, Moore, and the author, on the exponents of homotopy groups. K-theory 38 Bordism 40 Cohomotopy 42 The cohomology of groups 45 References 46 Introduction The study of symmetries on spaces has always been a major part of algebraic and geometric topology, but the systematic homotopical study of group actions is relatively recent.
The last decade has seen a great deal of activity in this. 10 Answers Algebraic K-theory originated in classical materials that connected class groups, unit groups and determinants, Brauer groups, and related things for rings of integers, fields, etc, and includes a lot of local-to-global principles.
Historically, the algebraic K-theory of a commutative ring R (what today is the “0th” algebraic K-theory group) was originally defined to be the Grothendieck group of its symmetric monoidal category of projective modules (under tensor product of modules).
Under the relation between modules and vector bundles. concocted from the given setup, and one deﬁnes a K-theory space associated to the geometric realization BCof this category. The K-theory groups are then the homotopy groups of the K-theory space.
In the ﬁrst chapter, we introduce the basic cast of characters: projective modules and vector bundles (over a topological space, and over a scheme).Algebraic K-theory and abstract homotopy theory Article in Advances in Mathematics (4) August with 24 Reads How we measure 'reads'.Another great reference is Hovey-Shipley-Smith Symmetric Spectra.
On the more modern side, there's Stefan Schwede's Symmetric Spectra Book Project. All these references contain phrasing in terms of model categories, which seem indispensible to modern homotopy theory. Good references are Hovey's book and Hirschhorn's book.