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The homotopy types of moment-angle complexes for flag complexes

The homotopy types of moment-angle complexes for flag complexes
The homotopy types of moment-angle complexes for flag complexes
We study the homotopy types of moment-angle complexes, or equivalently, of complements of coordinate subspace arrangements. The overall aim is to identify the simplicial complexes K for which the corresponding moment-angle complex Z_K has the homotopy type of a wedge of spheres or a connected sum of sphere products. When K is flag, we identify in algebraic and combinatorial terms those K for which Z_K is homotopy equivalent to a wedge of spheres, and give a combinatorial formula for the number of spheres in the wedge. This extends results of Berglund and Jollenbeck on Golod rings and homotopy theoretical results of the first and third authors. We also establish a connection between minimally non-Golod rings and moment-angle complexes Z_K which are homotopy equivalent to a connected sum of sphere products. We go on to show that for any flag complex K the loop space of Z_K is homotopy equivalent to a product of spheres and loops on spheres when localised rationally or at any prime not equal to 2.
0002-9947
6663-6682
Grbic, Jelena
daaea124-d4cc-4818-803a-2b0cb4362175
Panov, Taras
78d6f427-3f3d-481c-98be-6869370101aa
Theriault, Stephen
5e442ce4-8941-41b3-95f1-5e7562fdef80
Wu, Jie
541b9f29-928c-4fbd-9697-2f567d76feb6
Grbic, Jelena
daaea124-d4cc-4818-803a-2b0cb4362175
Panov, Taras
78d6f427-3f3d-481c-98be-6869370101aa
Theriault, Stephen
5e442ce4-8941-41b3-95f1-5e7562fdef80
Wu, Jie
541b9f29-928c-4fbd-9697-2f567d76feb6

Grbic, Jelena, Panov, Taras, Theriault, Stephen and Wu, Jie (2016) The homotopy types of moment-angle complexes for flag complexes. Transactions of the American Mathematical Society, 368 (9), 6663-6682. (doi:10.1090/tran/6578).

Record type: Article

Abstract

We study the homotopy types of moment-angle complexes, or equivalently, of complements of coordinate subspace arrangements. The overall aim is to identify the simplicial complexes K for which the corresponding moment-angle complex Z_K has the homotopy type of a wedge of spheres or a connected sum of sphere products. When K is flag, we identify in algebraic and combinatorial terms those K for which Z_K is homotopy equivalent to a wedge of spheres, and give a combinatorial formula for the number of spheres in the wedge. This extends results of Berglund and Jollenbeck on Golod rings and homotopy theoretical results of the first and third authors. We also establish a connection between minimally non-Golod rings and moment-angle complexes Z_K which are homotopy equivalent to a connected sum of sphere products. We go on to show that for any flag complex K the loop space of Z_K is homotopy equivalent to a product of spheres and loops on spheres when localised rationally or at any prime not equal to 2.

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Accepted/In Press date: 11 November 2015
e-pub ahead of print date: 12 November 2015
Published date: 2016
Organisations: Pure Mathematics

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Local EPrints ID: 396695
URI: http://eprints.soton.ac.uk/id/eprint/396695
ISSN: 0002-9947
PURE UUID: 693a74a8-7fed-490d-9421-1127091af39a
ORCID for Jelena Grbic: ORCID iD orcid.org/0000-0002-7164-540X
ORCID for Stephen Theriault: ORCID iD orcid.org/0000-0002-7729-5527

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Date deposited: 10 Jun 2016 15:35
Last modified: 15 Mar 2024 03:45

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Contributors

Author: Jelena Grbic ORCID iD
Author: Taras Panov
Author: Jie Wu

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