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Sunday, May 10, 2020 | History

2 edition of Nonabelian algebraic topology found in the catalog.

Nonabelian algebraic topology

filtered spaces, crossed complexes, cubical homotopy groupoids

by Brown, Ronald

  • 348 Want to read
  • 29 Currently reading

Published by European Mathematical Society in Zürich .
Written in English

    Subjects:
  • Algebraic topology,
  • Homotopy theory

  • Edition Notes

    Includes bibliographical references.

    StatementRonald Brown, Philip J.Higgins, Rafael Sivera, with contributions by Christopher D. Wensley and Sergei V. Soloviev
    SeriesEMS tracts in mathematics -- 15
    ContributionsHiggins, Philip J., 1926-, Sivera, Rafael
    The Physical Object
    Pagination668 pages :
    Number of Pages668
    ID Numbers
    Open LibraryOL25562160M
    ISBN 103037190833
    ISBN 109783037190838
    OCLC/WorldCa724312753

    In mathematics, higher category theory is the part of category theory at a higher order, which means that some equalities are replaced by explicit arrows in order to be able to explicitly study the structure behind those equalities. Higher category theory is often applied in algebraic topology (especially in homotopy theory), where one studies algebraic invariants of spaces, such as .   Then the book proper is split into three Parts the first two of which are roughly styled as, respectively, “develop[ing] that aspect of nonabelian algebraic topology related to the Seifert-Van Kampen Theorem in dimensions 1 and 2” (cf. p.3), and “obtain[ing] homotopical calculations using crossed complexes .

    This talk gave a sketch of the contents and background to a book with the title `Nonabelian algebraic topology' being written under support of a Leverhulme Emeritus Fellowship ( .   This talk gave a sketch of the contents and background to a book with the title `Nonabelian algebraic topology' being written under support of a Leverhulme Emeritus Fellowship () by the speaker and Rafael Sivera (Valencia). The aim is to give in one place a full account of work by R. Brown and P.J. Higgins since the s which defines.

    ISBN: OCLC Number: Description: xxxv, pages: illustrations (some color) ; 25 cm. Contents: Sets of base points, enter groupoids and 2-dimensional results --History --Homotopy theory and crossed modules --Basic algebra of crossed modules --Coproducts of crossed P-modules --Double groupoids and the 2-dimensional seifert . Thus algebraic topology becomes a major tool for the study of topological spaces, especially manifolds and CW-complexes. The main tools are the following. The fundamental group of a space X with base point x is a group (often nonabelian).


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Nonabelian algebraic topology by Brown, Ronald Download PDF EPUB FB2

This talk gave a sketch of a book with the title Nonabelian algebraic topology being written under support of a Leverhulme Emeritus Fellowship () by the speaker and Rafael Sivera (Valencia) [6].

The aim is to give in one place a full account of work by R. Brown and. The book has no homology theory, so it contains only one initial part of algebraic topology. BUT, another part of algebraic topology is in the new jointly authored book Nonabelian Algebraic Topology: filtered spaces, crossed complexes, cubical homotopy groupoids (NAT) published in by the European Mathematical Society.

The print version is. The main theme of this book is that the use of filtered spaces rather than just topological spaces allows the development of basic algebraic topology in terms of higher homotopy groupoids; these algebraic structures better reflect the geometry of subdivision and composition than those commonly in by: In mathematics, nonabelian algebraic topology studies an aspect of algebraic topology that involves (inevitably noncommutative) higher-dimensional algebras.

Many of the higher-dimensional algebraic structures are noncommutative and, therefore, their study is a very significant part of nonabelian category theory, and also of Nonabelian Algebraic Topology.

This entry is about the book. Ronnie Brown, Philip Higgins, Rafael Sivera, Nonabelian Algebraic Topology: filtered spaces, crossed complexes, cubical homotopy groupoids Tracts in Mathemat European Mathematical Society, web, from which the full pdf is available.; The publication details of the book are as follows: ISBNDOI / The crossed Nonabelian algebraic topology book theory has been deeply analyzed by Brown et al.'s book "Nonabelian Algebraic Topology", [5], and in the Nonabelian algebraic topology book by Porter "The Crossed Menagerie" [16].

As an application of cyclic. Nonabelian Algebraic Topology by Ronald Brown, Philip J. Higgins, and Rafael Sivera The following account is adapted from a Proposal for a Leverhulme Emeritus Fellowship for Brown, ; the chosen referees were Professor A. Bak (Bielefeld) and Professor J.P.

May (Chicago), and the proposal was fully funded. Ah ha great question. Undoubtedly, the best reference on topology is "Topology" by Munkres: Yes. One overall theme of this book is the use for the foundations of algebraic topology of some higher categorical structures, which allow for the application of higher dimensional nonabelian methods to certain local-to-global problems.

Abstract: This talk gave a sketch of the contents and background to a book with the title `Nonabelian algebraic topology' being written under support of a Leverhulme Emeritus Fellowship () by the speaker and Rafael Sivera (Valencia).

The aim is to give in one place a full account of work by R. Brown and P.J. Higgins since the s which defines and applies Cited by: I have made a note of some problems in the area of Nonabelian algebraic topology and homological algebra inand in Chapter 16 of the book in the same area and advertised here, with free pdf, there is a note of 32 problems and questions in this area which had occurred to problems may well seem "narrow", and/or "out-of-line" of current trends, but I.

Here it is — the magnum opus of cubical methods in algebraic topology. Ronald Brown, Philip J. Higgins and Rafael Sivera, Nonabelian algebraic topology: homotopy groupoids and filtered spaces.

It’s still just a preliminary version, but it’s pages long, and packed with good stuff — and it’s free!. Grab a copy. Nonabelian algebraic topology. In the book “Nonabelian algebraic topology: filtered spaces, crossed complexes, cubical homotopy groupoids” by R.

Brown, P.J. Higgins and R. Sivera, EMS Tracts in Mathematics vol 15 (), Chapter 16 on “Future Directions?” has 32 problems arising out of the previous material, and suggesting areas for development. ^ Non-Abelian Algebraic Topology book Archived at the Wayback Machine ^ Nonabelian Algebraic Topology: Higher homotopy groupoids of filtered spaces ^ Brown, R.; et al.

Nonabelian Algebraic Topology: Higher homotopy groupoids of filtered spaces (in press). [permanent dead link]. His latest publication is R. Brown, P.J. Higgins, R. Sivera, Nonabelian algebraic topology: filtered spaces, crossed complexes, cubical homotopy groupoids, EMS Tracts in Mathematics Vol.

15, pages. (August ) which gives an exposition of aspects of 40 years of research on developing applications of higher groupoids in by:   This talk gave a sketch of the contents and background to a book with the title `Nonabelian algebraic topology' being written under support of a Leverhulme Emeritus Fellowship () by the speaker and Rafael Sivera (Valencia).

The aim is to give in one place a full account of work by R. Brown and P.J. Higgins since the s which defines and applies Cited by: In higher-dimensional algebra (HDA), a double groupoid is a generalisation of a one-dimensional groupoid to two dimensions, and the latter groupoid can be considered as a special case of a category with all invertible arrows, or morphisms.

Double groupoids are often used to capture information about geometrical objects such as higher-dimensional manifolds (or n-dimensional. The book "Nonabelian Algebraic Topology" cited below has a Section on cubical versions of the Dold–Kan theorem, and relates them to a previous equivalence of categories between cubical omega-groupoids and crossed complexes, which is fundamental to.

This is a survey of central results in nonabelian algebraic topology. We present how the homotopy category of homotopy \(n\)-types and a certain localization of the category of crossed \(n\)-cubes of groups are functor inducing this equivalence satisfy a generalized Seifert-van Kampen theorem, in that it preserves connectivity and colimits of Author: Renato Vieira.

Brown, Ph.J. Higgins, R. Sivera: “Nonabelian Algebraic Topology” modulo Peiffer identities (identities of the kind (1) above, independently of the par-ticular presentation), yield the “correct” relations for N as an F-group generated by R. There are no non-trivial identities in this sense if and only if the second absolute.

See section in Chapter I of Serre's book on Galois cohomology for the Galois case, Milne's "Etale cohomology" book for generalization with flat and \'etale topologies, and Appendix B in my paper on "Finiteness theorems for algebraic groups over function fields" for a concrete fleshing out of the dictionary between the torsor and Galois.Get this from a library!

Nonabelian algebraic topology: filtered spaces, crossed complexes, cubical homotopy groupoids. [Ronald Brown; Philip J Higgins; Rafael Sivera] -- The main theme of this book is that the use of filtered spaces rather than just topological spaces allows the development of basic algebraic topology in terms of higher homotopy groupoids; these.

Nonabelian Algebraic Topology: Filtered Spaces, Crossed Complexes, Cubical Homotopy Groupoids Share this page The structure of the book is intended to make it useful to a wide class of students and researchers for learning and evaluating these methods, primarily in algebraic topology but also in higher category theory and its applications.