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A homotopy theoretical generalization of the Bestvina-Brady construction

A homotopy theoretical generalization of the Bestvina-Brady construction
A homotopy theoretical generalization of the Bestvina-Brady construction
By using the notion of polyhedral products (X,A)^K, we recognise the Bestvina–Brady construction [4] as the fundamental group of the homotopy fibre of (S^1,*)^L-->S^1, where L is a flag complex. We generalise their construction by studying the homotopy fibre F of (S^1,*)^L--> (S^1,*)^K for an arbitrary simplicial complex L and K an (m-1)-dimensional simplex. For a particular class of simplicial complexes L, we describe the homology of F, its fixed points, and maximal invariant quotients for coordinate subgroups of Z^m. This generalises the work of Leary and Saadetoğlu [13] who studied the case when m=1.
polyhedral products, Bestvina-Brady
43-53
Grbic, Jelena
daaea124-d4cc-4818-803a-2b0cb4362175
Intermont, Michele
d9cdb0ed-612e-4f78-bff1-9601c9618650
Laude, Isabelle
0a7f2215-a1ae-406a-a135-705ec7b4bc59
Vidaurre, Elizabeth
73c6d22b-5822-45bf-9eaa-bb3a1cc0a5e4
Grbic, Jelena
daaea124-d4cc-4818-803a-2b0cb4362175
Intermont, Michele
d9cdb0ed-612e-4f78-bff1-9601c9618650
Laude, Isabelle
0a7f2215-a1ae-406a-a135-705ec7b4bc59
Vidaurre, Elizabeth
73c6d22b-5822-45bf-9eaa-bb3a1cc0a5e4

Grbic, Jelena, Intermont, Michele, Laude, Isabelle and Vidaurre, Elizabeth (2018) A homotopy theoretical generalization of the Bestvina-Brady construction. Topology and its Applications, 235, 43-53. (doi:10.1016/j.topol.2017.12.007).

Record type: Article

Abstract

By using the notion of polyhedral products (X,A)^K, we recognise the Bestvina–Brady construction [4] as the fundamental group of the homotopy fibre of (S^1,*)^L-->S^1, where L is a flag complex. We generalise their construction by studying the homotopy fibre F of (S^1,*)^L--> (S^1,*)^K for an arbitrary simplicial complex L and K an (m-1)-dimensional simplex. For a particular class of simplicial complexes L, we describe the homology of F, its fixed points, and maximal invariant quotients for coordinate subgroups of Z^m. This generalises the work of Leary and Saadetoğlu [13] who studied the case when m=1.

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Accepted/In Press date: 3 October 2017
e-pub ahead of print date: 6 December 2017
Published date: 15 February 2018
Keywords: polyhedral products, Bestvina-Brady

Identifiers

Local EPrints ID: 416984
URI: https://eprints.soton.ac.uk/id/eprint/416984
PURE UUID: 6f158222-512a-40cb-87ce-07873c1d7bfb

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Date deposited: 16 Jan 2018 17:30
Last modified: 11 Apr 2018 16:31

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Contributors

Author: Jelena Grbic
Author: Michele Intermont
Author: Isabelle Laude
Author: Elizabeth Vidaurre

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