Algebraic Topology of Finite Topological Spaces and Applications
(Sprache: Englisch)
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...
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Klappentext zu „Algebraic Topology of Finite Topological Spaces and Applications “
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.
Inhaltsverzeichnis zu „Algebraic Topology of Finite Topological Spaces and Applications “
1 Preliminaries2 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
Bibliographische Angaben
- Autor: Jonathan A. Barmak
- 2011, 2011, XVII, 170 Seiten, Maße: 15,5 x 23,5 cm, Kartoniert (TB), Englisch
- Verlag: Springer, Berlin
- ISBN-10: 3642220029
- ISBN-13: 9783642220029
- Erscheinungsdatum: 24.08.2011
Sprache:
Englisch
Rezension zu „Algebraic Topology of Finite Topological Spaces and Applications “
From the reviews:"This book illustrates convincingly the idea that the study of finite non-Hausdorff spaces from a homotopical point of view is useful in many areas and can even be used to study well-known problems in classical algebraic topology. ... This book is a revised version of the PhD Thesis of the author. ... All the concepts introduced with the chapters are usefully illustrated by examples and the recollection of all these results gives a very nice introduction to a domain of growing interest." (Etienne Fieux, Zentralblatt MATH, Vol. 1235, 2012)
Pressezitat
From the reviews:"This book deals with the algebraic topology of finite topological spaces and its applications, and includes well-known results on finite spaces and original results developed by the author. The book is self-contained and well written. It is understandable and enjoyable to read. It contains a lot of examples and figures which help the readers to understand the theory." (Fumihiro Ushitaki, Mathematical Reviews, March, 2014)
"This book illustrates convincingly the idea that the study of finite non-Hausdorff spaces from a homotopical point of view is useful in many areas and can even be used to study well-known problems in classical algebraic topology. ... This book is a revised version of the PhD Thesis of the author. ... All the concepts introduced with the chapters are usefully illustrated by examples and the recollection of all these results gives a very nice introduction to a domain of growing interest." (Etienne Fieux, Zentralblatt MATH, Vol. 1235, 2012)
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