Published on *Max Planck Institute for Mathematics* (http://www.mpim-bonn.mpg.de)

Posted in

- Talk [1]

Speaker:

Corey Bregman
Affiliation:

University of Southern Maine
Date:

Mon, 31/05/2021 - 15:30 - 16:30 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 [3]

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.

**Links:**

[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39

[2] http://www.mpim-bonn.mpg.de/TopologySeminar

[3] https://nextcloud.mpim-bonn.mpg.de/s/Tq9bsCWsAJrRiNk