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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
We give various bounds for the Lusternik-Schnirelmann category of moment-angle complexes and show how this relates to vanishing of Massey products in $\mathrm{Tor}^+_{R[v_1,\ldots,v_n]}(R[K],R)$. In particular, we characterise the Lusternik-Schnirelmann category of moment-angle manifolds $\mathcal{Z}_K$ over triangulated $d$-spheres $K$ for $d\leq 2$, 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 $H^*(\mathcal{Z}_K)$, as well as a certain generalisation of the Golod property. Some applications include information about the category and vanishing of Massey products for moment-angle complexes over fullerenes and $k$-neighbourly complexes.
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. Author's Original, 1-21. (Submitted)

Record type: Article

Abstract

We give various bounds for the Lusternik-Schnirelmann category of moment-angle complexes and show how this relates to vanishing of Massey products in $\mathrm{Tor}^+_{R[v_1,\ldots,v_n]}(R[K],R)$. In particular, we characterise the Lusternik-Schnirelmann category of moment-angle manifolds $\mathcal{Z}_K$ over triangulated $d$-spheres $K$ for $d\leq 2$, 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 $H^*(\mathcal{Z}_K)$, as well as a certain generalisation of the Golod property. Some applications include information about the category and vanishing of Massey products for moment-angle complexes over fullerenes and $k$-neighbourly complexes.

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Submitted date: 22 April 2016
Organisations: Mathematical Sciences

Identifiers

Local EPrints ID: 398085
URI: https://eprints.soton.ac.uk/id/eprint/398085
PURE UUID: f0454e95-8bba-4f6b-b981-6bdcaa894d27

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Date deposited: 18 Jul 2016 09:09
Last modified: 05 Oct 2018 12:06

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