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Algebraic Topology of Finite Topological Spaces and Applications
Taschenbuch von Jonathan A. Barmak
Sprache: Englisch

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Beschreibung
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.
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.
Zusammenfassung

It is the first complete exposition of the topic

Has applications to the study of two long-standing conjectures

It is self-contained

Includes supplementary material: [...]

Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 2011
Fachbereich: Topologie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Reihe: Lecture Notes in Mathematics
Inhalt: xvii
170 S.
35 s/w Illustr.
170 p. 35 illus.
ISBN-13: 9783642220029
ISBN-10: 3642220029
Sprache: Englisch
Herstellernummer: 80065574
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Barmak, Jonathan A.
Hersteller: Springer-Verlag GmbH
Springer Berlin Heidelberg
Lecture Notes in Mathematics
Maße: 235 x 155 x 11 mm
Von/Mit: Jonathan A. Barmak
Erscheinungsdatum: 24.08.2011
Gewicht: 0,3 kg
Artikel-ID: 106950784
Zusammenfassung

It is the first complete exposition of the topic

Has applications to the study of two long-standing conjectures

It is self-contained

Includes supplementary material: [...]

Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 2011
Fachbereich: Topologie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Reihe: Lecture Notes in Mathematics
Inhalt: xvii
170 S.
35 s/w Illustr.
170 p. 35 illus.
ISBN-13: 9783642220029
ISBN-10: 3642220029
Sprache: Englisch
Herstellernummer: 80065574
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Barmak, Jonathan A.
Hersteller: Springer-Verlag GmbH
Springer Berlin Heidelberg
Lecture Notes in Mathematics
Maße: 235 x 155 x 11 mm
Von/Mit: Jonathan A. Barmak
Erscheinungsdatum: 24.08.2011
Gewicht: 0,3 kg
Artikel-ID: 106950784
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