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2019 Classifying spaces from Ore categories with Garside families
Stefan Witzel
Algebr. Geom. Topol. 19(3): 1477-1524 (2019). DOI: 10.2140/agt.2019.19.1477

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 .

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Stefan Witzel. "Classifying spaces from Ore categories with Garside families." Algebr. Geom. Topol. 19 (3) 1477 - 1524, 2019. https://doi.org/10.2140/agt.2019.19.1477

Information

Received: 27 April 2018; Revised: 1 November 2018; Accepted: 1 November 2018; Published: 2019
First available in Project Euclid: 29 May 2019

zbMATH: 07142604
MathSciNet: MR3954289
Digital Object Identifier: 10.2140/agt.2019.19.1477

Subjects:
Primary: 57M07
Secondary: 20F36, 20F65

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.19 • No. 3 • 2019
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