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Toric homotopy theory

Toric homotopy theory
Toric homotopy theory

These notes describe some of the homotopy theory surrounding Davis-Januszkiewicz spaces, moment-angle complexes and their generalizations to polyhedral products. These spaces are defined by gluing together prod- ucts formed from pairs of spaces (X, A), where the gluing is determined by the faces of a simplicial complex K. The emphasis is on determining homotopy types - of the spaces themselves, their suspensions and their based loop spaces - and showing how these homotopy types depend on a beautiful interplay between the topology of the pairs (X, A) and the combinatorics of the simplicial complex K.

1793-0758
1-66
World Scientific Publishing Co
Theriault, Stephen
5e442ce4-8941-41b3-95f1-5e7562fdef80
Darby, Alastair
Grbic, Jelena
Lu, Zhi
Wu, Jie
Theriault, Stephen
5e442ce4-8941-41b3-95f1-5e7562fdef80
Darby, Alastair
Grbic, Jelena
Lu, Zhi
Wu, Jie

Theriault, Stephen (2017) Toric homotopy theory. In, Darby, Alastair, Grbic, Jelena, Lu, Zhi and Wu, Jie (eds.) Combinatorial and Toric Homotopy : Introductory Lectures. (Lecture Notes Series, Institute for Mathematical Sciences, , (doi:10.1142/9789813226579_0001), 35) World Scientific Publishing Co, pp. 1-66. (doi:10.1142/9789813226579_0001).

Record type: Book Section

Abstract

These notes describe some of the homotopy theory surrounding Davis-Januszkiewicz spaces, moment-angle complexes and their generalizations to polyhedral products. These spaces are defined by gluing together prod- ucts formed from pairs of spaces (X, A), where the gluing is determined by the faces of a simplicial complex K. The emphasis is on determining homotopy types - of the spaces themselves, their suspensions and their based loop spaces - and showing how these homotopy types depend on a beautiful interplay between the topology of the pairs (X, A) and the combinatorics of the simplicial complex K.

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Accepted/In Press date: 24 October 2017
e-pub ahead of print date: October 2017
Published date: December 2017

Identifiers

Local EPrints ID: 417494
URI: http://eprints.soton.ac.uk/id/eprint/417494
ISSN: 1793-0758
PURE UUID: 7c8fc081-56d8-421b-b905-0355494e5a45
ORCID for Stephen Theriault: ORCID iD orcid.org/0000-0002-7729-5527

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Date deposited: 01 Feb 2018 17:30
Last modified: 20 Jul 2019 00:40

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