A homotopy theoretical generalisation of the Bestvina-Brady construction

作者：Grbic Jelena^*; Intermont Michele; Laude Isabelle; Vidaurre Elizabeth

来源：Topology and Its Applications, 2018, 235: 43-53.

DOI：10.1016/j.topol.2017.12.007

• Polyhedral product
• Homotopy fibre
• Bestvina-Brady group

By using the notion of polyhedral products ((X) under bar, (A) under bar)(K), we recognise the Bestvina-Brady construction [4] as the fundamental group of the homotopy fibre of (S-1, *)(L) -> S-1, where L is a flag complex. We generalise their construction by studying the homotopy fibre F of (S-1, *)(L) -> (S-1, *)(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 Z(m). This generalises the work of Leary and Saadetoglu [13] who studied the case when m = 1.

• 出版日期2018-2-15