Volume 19, issue 3 (2019)

 Recent Issues
 The Journal About the Journal Editorial Board Editorial Interests Subscriptions Submission Guidelines Submission Page Policies for Authors Ethics Statement ISSN (electronic): 1472-2739 ISSN (print): 1472-2747 Author Index To Appear Other MSP Journals
Classifying spaces from Ore categories with Garside families

Stefan Witzel

Algebraic & Geometric Topology 19 (2019) 1477–1524
Abstract

We describe how an Ore category with a Garside family can be used to construct a classifying space for its fundamental group(s). The construction simultaneously generalizes Brady’s classifying space for braid groups and the Stein–Farley complexes used for various relatives of Thompson’s groups. It recovers the fact that Garside groups have finite classifying spaces.

We describe the categories and Garside structures underlying certain Thompson groups. The indirect product of categories is introduced and used to construct new categories and groups from known ones. As an illustration of our methods we introduce the group braided $T$ and show that it is of type ${F}_{\infty }$.

Keywords
Thompson groups, braid groups, finiteness properties, classifying spaces, Ore categories, Garside structures
Mathematical Subject Classification 2010
Primary: 57M07
Secondary: 20F36, 20F65