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.