36th Summer Topology Conference

July 18-22, 2022

University of Vienna, Department of Mathematics
Oskar-Morgenstern-Platz 1, 1090 Vienna, AUSTRIA

"Braided Thompson groups and their quasimorphisms"

Fournier-Facio, Francesco

Braided Thompson groups are very interesting examples in geometric group theory. They arise as left-orderable groups with combinations of interesting property, but also as subgroups of the mapping class group of the plane minus a Cantor set. Since they are built out of braid groups and Thompson groups, when trying to establish a property it is often not clear which side will prevail. We explore quasimorphisms of some braided Thompson groups, and see that by slightly changing the groups we can drastically modify their behaviour, so that some of these groups conform to the braid part, and others to the Thompson part. Joint with Yash Lodha and Matthew Zaremsky.

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