2 edition of **Generalized cohomology and K-theory** found in the catalog.

Generalized cohomology and K-theory

M. Bendersky

- 308 Want to read
- 32 Currently reading

Published
**1972** by Aarhus universitet, Matematisk institut] in [Aarhus, Denmark .

Written in English

- Homology theory.,
- K-theory.

**Edition Notes**

Bibliography: leaves 104-106.

Statement | [By] M. Bendersky. |

Series | Lecture notes series -- no. 33, Lecture notes series (Aarhus universitet. Matematisk institut) -- no. 33. |

Classifications | |
---|---|

LC Classifications | QA612.3 .B433 |

The Physical Object | |

Pagination | 106 p. ; |

Number of Pages | 106 |

ID Numbers | |

Open Library | OL21237089M |

Examples include etale cohomology and etale K-theory. Apr 10, Jorge Becerra: The Hopf invariant one problem. Starting in the s, sheaf cohomology has become a central part of algebraic geometry and complex analysispartly because of the importance of the sheaf of regular functions or the sheaf of holomorphic functions. Thus this book might be regarded as a fairly self-contained introduction to a "generalized cohomology theory". In addition, several applications of the type described above are included.

This book should be of interest to all researchers working in fields related to algebraic K-theory. Introduced by Donald W. Axioms, first examples. Lecture Notes in german.

The techniques presented here are essentially combinatorial, and hence algebraic. Starting in the s, sheaf cohomology has become a central part of algebraic geometry and complex analysispartly because of the importance of the sheaf of regular functions or the sheaf of holomorphic functions. K theory with coefficients[ edit ] Spectrum: KG G is some abelian group; for example the localization Z p at the prime p. May 1, Bjarne Kosmeijer: Thom isomorphisms in K-theory and in cohomology. KSp0 X is the ring of stable equivalence classes of quaternionic vector bundles over X.

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The treatment includes, for the purpose of adequately Generalized cohomology and K-theory book with cup product structures, a development of stable homotopy theory for n-fold spectra, which is then promoted to the level of presheaves of n-fold spectra. Keywords Algebraic topology Compact space Homotopy Homotopy group K-theory algebra applications of K-Theory homotopy theory topology vector bundle Authors and affiliations.

The book is intended to serve as an introduction to the subject for mathematicians who do not have advanced knowledge of algebraic topology. This book gives new and complete proofs of both Thomason's descent theorem for Bott periodic K-theory and the Generalized cohomology and K-theory book descent theorem.

An extensive background in traditional stable homotopy theory is not assumed. The book will be very useful for any researcher interested in subjects related to algebraic K-theory. It supplies details for some crucial theorems and directs the reader to excellent treatments of quoted material.

Homology and cohomology with integer coefficients. Grothendieck in his formulation of the Riemann- Roch theorem. Material: Remainder of the proof of the product theorem, Bott periodicity as a consequence.

K0 X is the ring of stable equivalence classes of complex vector bundles over X. Mar 27, Thomas Blom: Adams operations. Homology and cohomology with mod p coefficients. Readership Graduate students and research mathematicians interested in algebraic topology.

Lecture Notes in german. Despite the purely algebraic nature of the statement, the proof, that was found by John Frank Adams inis based on results from algebraic topology. Jorge's notes. These theories come under the common name of generalized homology or cohomology theories.

Coefficient ring: For ku, the coefficient ring is the ring of polynomials over Z on a single class v1 in dimension 2. In their book, Foundations of Algebraic Topology, they proved that the existing homology and cohomology theories did indeed satisfy their axioms.

Examples include etale cohomology and etale K-theory.

Generalized cohomology and K-theory book G is the integers, the rationals, the reals, the complex numbers, or the integers mod a prime p.Topological K-theory has become an important tool in tjarrodbonta.com 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 tjarrodbonta.comer, it is possible to derive a substantial part of stable homotopy theory from K-theory.

Buy K-Theory: An Introduction (Classics in Mathematics) on tjarrodbonta.com FREE SHIPPING on qualified orders Skip to main content. Try Prime Hello, Sign in Account classes of maps and homotopy tjarrodbonta.com this book might be regarded as a fairly self-contained introduction to a "generalized cohomology theory".

Cited by: Course description > Topological K-theory, the first generalized cohomology theory to be studied thoroughly, was introduced in a paper by Atiyah and Hirzebruch, where they adapted the work of Grothendieck on algebraic varieties to a topological tjarrodbonta.com that time, topological K-theory has become a powerful and indispensable tool in topology, differential geometry, and index theory.This can be seen as the collapsing of the previous pdf sequence adapted to K theory at the stage 1.

My question is: is there a way to build a MV spectral sequence for topological K theory? kt.k-theory-and-homology spectral-sequences.A generalized cohomology theory has the data of a spectrum that defines it.

Topological K theory of X is studied by download pdf X into what we call KU and algebraic K theory by KC. The way to say the relation is there is a map of spectra between algebraic K theory spectrum of complex numbers to the spectrum that defines complex topological K theory.A generalized cohomology ebook has the data of a spectrum that defines it.

Topological K theory of X is studied ebook mapping X into what we call KU and algebraic K theory by KC. The way to say the relation is there is a map of spectra between algebraic K theory spectrum of complex numbers to the spectrum that defines complex topological K theory.