A homotopy theoretical generalisation of the Bestvina–Brady construction

Jelena Grbić; Michele Intermont; Elizabeth Vidaurre; Isabelle Laude

doi:10.1016/j.topol.2017.12.007

A homotopy theoretical generalisation of the Bestvina–Brady construction

Jelena Grbić
, Michele Intermont
, Elizabeth Vidaurre
, Isabelle Laude

Mathematics and Computer Studies

Research & Scholarship: Contribution to journal › Article › peer-review

Abstract

<div class="line" id="line-7"> 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, &lowast;)L → S1, where L is a flag complex. We generalise their construction by studying the homotopy fibre F of (S1, &lowast;)L → (S1, &lowast;)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 Saadeto&gbreve;lu [13] who studied the case when m = 1.</div>

Original language	English
Pages (from-to)	43-53
Number of pages	11
Journal	Topology and its Applications
Volume	235
DOIs	https://doi.org/10.1016/j.topol.2017.12.007
State	Published - Feb 15 2018

ASJC Scopus Subject Areas

Geometry and Topology

Keywords

Bestvina–Brady group
Homotopy fibre
Polyhedral product

Access to Document

10.1016/j.topol.2017.12.007

Cite this

@article{540f0d904fc7455e9a3cca1a5b5d0ea3,

title = "A homotopy theoretical generalisation of the Bestvina–Brady construction",

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, \&lowast;)L \→ S1, where L is a flag complex. We generalise their construction by studying the homotopy fibre F of (S1, \&lowast;)L \→ (S1, \&lowast;)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 Saadeto\&gbreve;lu [13] who studied the case when m = 1.",

keywords = "Bestvina–Brady group, Homotopy fibre, Polyhedral product",

author = "Jelena Grbi{\'c} and Michele Intermont and Elizabeth Vidaurre and Isabelle Laude",

note = "Publisher Copyright: {\textcopyright} 2017 Elsevier B.V.",

year = "2018",

month = feb,

day = "15",

doi = "10.1016/j.topol.2017.12.007",

language = "English",

volume = "235",

pages = "43--53",

journal = "Topology and its Applications",

issn = "0166-8641",

}

TY - JOUR

T1 - A homotopy theoretical generalisation of the Bestvina–Brady construction

AU - Grbić, Jelena

AU - Intermont, Michele

AU - Vidaurre, Elizabeth

AU - Laude, Isabelle

PY - 2018/2/15

Y1 - 2018/2/15

N2 - 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, &lowast;)L → S1, where L is a flag complex. We generalise their construction by studying the homotopy fibre F of (S1, &lowast;)L → (S1, &lowast;)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 Saadeto&gbreve;lu [13] who studied the case when m = 1.

AB - 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, &lowast;)L → S1, where L is a flag complex. We generalise their construction by studying the homotopy fibre F of (S1, &lowast;)L → (S1, &lowast;)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 Saadeto&gbreve;lu [13] who studied the case when m = 1.

KW - Bestvina–Brady group

KW - Homotopy fibre

KW - Polyhedral product

U2 - 10.1016/j.topol.2017.12.007

DO - 10.1016/j.topol.2017.12.007

M3 - Article

SN - 0166-8641

VL - 235

SP - 43

EP - 53

JO - Topology and its Applications

JF - Topology and its Applications

ER -