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LS-category of moment-angle manifolds, Massey products, and a generalisation of the Golod property

LS-category of moment-angle manifolds, Massey products, and a generalisation of the Golod property
LS-category of moment-angle manifolds, Massey products, and a generalisation of the Golod property
This paper is obtained as as synergy of homotopy theory, commutative algebra and combinatorics. We give various bounds for the Lusternik-Schnirelmann category of moment-angle complexes and show how this relates to vanishing of Massey products in Tor+R[v1,...,vn] (R [K], R) for the Stanley-Reisner ring R[K]. In particular, we characterise the Lusternik-Schnirelmann category of moment-angle manifolds ZK over triangulated d-spheres K for d ≤ 2, as well as higher dimension spheres built up via connected sum, join, and vertex doubling operations. This characterisation is given in terms of the combinatorics of K, the cup product length of H* (ZK), as well as a certain generalisation of the Golod property. As an application, we describe conditions for vanishing of Massey products in the case of fullerenes and k-neighbourly complexes.
0002-9947
1-21
Beben, Piotr
a74d3e1f-52e0-4dc6-8f20-9c1628a20d2b
Grbic, Jelena
daaea124-d4cc-4818-803a-2b0cb4362175
Beben, Piotr
a74d3e1f-52e0-4dc6-8f20-9c1628a20d2b
Grbic, Jelena
daaea124-d4cc-4818-803a-2b0cb4362175

Beben, Piotr and Grbic, Jelena (2016) LS-category of moment-angle manifolds, Massey products, and a generalisation of the Golod property. Transactions of the American Mathematical Society, 1-21. (Submitted)

Record type: Article

Abstract

This paper is obtained as as synergy of homotopy theory, commutative algebra and combinatorics. We give various bounds for the Lusternik-Schnirelmann category of moment-angle complexes and show how this relates to vanishing of Massey products in Tor+R[v1,...,vn] (R [K], R) for the Stanley-Reisner ring R[K]. In particular, we characterise the Lusternik-Schnirelmann category of moment-angle manifolds ZK over triangulated d-spheres K for d ≤ 2, as well as higher dimension spheres built up via connected sum, join, and vertex doubling operations. This characterisation is given in terms of the combinatorics of K, the cup product length of H* (ZK), as well as a certain generalisation of the Golod property. As an application, we describe conditions for vanishing of Massey products in the case of fullerenes and k-neighbourly complexes.

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Submitted date: 31 October 2016
Organisations: Pure Mathematics

Identifiers

Local EPrints ID: 402254
URI: https://eprints.soton.ac.uk/id/eprint/402254
ISSN: 0002-9947
PURE UUID: 5d264d61-4cf7-4f9c-9704-d82772e62ca2

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Date deposited: 04 Nov 2016 11:34
Last modified: 16 Jul 2018 16:31

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