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From flat doughnuts to outer space: a classifying space odyssey

Posted in
Speaker: 
Jean-Pierre Mutanguha
Affiliation: 
MPIM
Date: 
Mon, 2021-05-17 14:00 - 15:00
Parent event: 
MPIM Topology Seminar

Meeting ID: 916 5855 1117
Password: as before.
Contact: Aru Ray, Tobias Barthel,Viktoriya Ozornova
Slides: are attached on the Talk's page or see our Nextcloud
 

In this talk, we construct an outer space for right-angled Artin groups (RAAGs) generalising that of free groups.  To do this, we will describe a family of locally CAT(0) spaces built from parallelotopes, whose fundamental group is a given RAAG.  Moving around in the moduli space of all such metrics, we will be able to realize any automorphism, and thus obtain an action of the outer automorphism group of the RAAG.  We show that the moduli space is finite dimensional, contractible and that the action is proper.  Time permitting, we will outline recent work studying the fixed sets of finite subgroups, and discuss open problems.  This is joint work with Ruth Charney and Karen Vogtmann.

 

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