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
15 February 2018
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, .
(doi:10.1016/j.topol.2017.12.007).
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: http://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: 16 Mar 2024 06:06
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Contributors
Author:
Michele Intermont
Author:
Isabelle Laude
Author:
Elizabeth Vidaurre
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