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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∞.
Keywords: Thompson groups, braid groups, finiteness properties, classifying spaces, Ore categories, Garside structures
Witzel, Stefan 1
@article{10_2140_agt_2019_19_1477,
author = {Witzel, Stefan},
title = {Classifying spaces from {Ore} categories with {Garside} families},
journal = {Algebraic and Geometric Topology},
pages = {1477--1524},
publisher = {mathdoc},
volume = {19},
number = {3},
year = {2019},
doi = {10.2140/agt.2019.19.1477},
url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2019.19.1477/}
}
TY - JOUR AU - Witzel, Stefan TI - Classifying spaces from Ore categories with Garside families JO - Algebraic and Geometric Topology PY - 2019 SP - 1477 EP - 1524 VL - 19 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.2140/agt.2019.19.1477/ DO - 10.2140/agt.2019.19.1477 ID - 10_2140_agt_2019_19_1477 ER -
%0 Journal Article %A Witzel, Stefan %T Classifying spaces from Ore categories with Garside families %J Algebraic and Geometric Topology %D 2019 %P 1477-1524 %V 19 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.2140/agt.2019.19.1477/ %R 10.2140/agt.2019.19.1477 %F 10_2140_agt_2019_19_1477
Witzel, Stefan. Classifying spaces from Ore categories with Garside families. Algebraic and Geometric Topology, Tome 19 (2019) no. 3, pp. 1477-1524. doi: 10.2140/agt.2019.19.1477
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