
Article
A homotopy theoretical generalisation of the Bestvina–Brady construction
Topology and its Applications
(2018)
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 (S1, ∗)L → S1, where L is a flag complex. We generalise their construction by studying the homotopy fibre F of (S1, ∗)L → (S1, ∗)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 Zm. This generalises the work of Leary and Saadetoğlu [13] who studied the case when m = 1.
Keywords
- Polyhedral product,
- Bestvina–Brady group,
- Homotopy fibre
Disciplines
Publication Date
February, 2018
DOI
10.1016/j.topol.2017.12.007
Citation Information
Jelena Grbić, Michele Intermont, Elizabeth Vidaurre and Isabelle Laude. "A homotopy theoretical generalisation of the Bestvina–Brady construction" Topology and its Applications Vol. 235 Iss. Virtual Special Issue (2018) p. 43 - 53 Available at: http://works.bepress.com/elizabeth-vidaurre/4/