Record Nr.

UNINA9910484422303321

Autore

Barmak Jonathan A

Titolo

Algebraic Topology of Finite Topological Spaces and Applications [[electronic resource] /] / by Jonathan A. Barmak

Pubbl/distr/stampa


Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2011

ISBN

3-642-22003-7

Edizione

[1st ed. 2011.]

Descrizione fisica

1 online resource (XVII, 170p. 35 illus.)

Collana

Lecture Notes in Mathematics, , 0075-8434 ; ; 2032

Disciplina

514.2

Soggetti

Algebraic topology

Combinatorics

Convex geometry

Discrete geometry

Algebra

Ordered algebraic structures

Manifolds (Mathematics)

Complex manifolds

Discrete mathematics

Algebraic Topology

Convex and Discrete Geometry

Order, Lattices, Ordered Algebraic Structures

Manifolds and Cell Complexes (incl. Diff.Topology)

Discrete Mathematics

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Bibliographic Level Mode of Issuance: Monograph

Nota di bibliografia

Includes bibliographical references and index.

Nota di contenuto

1 Preliminaries -- 2 Basic topological properties of finite spaces -- 3 Minimal finite models -- 4 Simple homotopy types and finite spaces -- 5 Strong homotopy types -- 6 Methods of reduction -- 7 h-regular complexes and quotients -- 8 Group actions and a conjecture of Quillen -- 9 Reduced lattices -- 10 Fixed points and the Lefschetz number -- 11 The Andrews-Curtis conjecture.

Sommario/riassunto

This volume deals with the theory of finite topological spaces and its relationship with the homotopy and simple homotopy theory of

polyhedra. The interaction between their intrinsic combinatorial and topological structures makes finite spaces a useful tool for studying problems in Topology, Algebra and Geometry from a new perspective. In particular, the methods developed in this manuscript are used to study Quillen’s conjecture on the poset of p-subgroups of a finite group and the Andrews-Curtis conjecture on the 3-deformability of contractible two-dimensional complexes. This self-contained work constitutes the first detailed exposition on the algebraic topology of finite spaces. It is intended for topologists and combinatorialists, but it is also recommended for advanced undergraduate students and graduate students with a modest knowledge of Algebraic Topology.