"Braided Thompson groups and their quasimorphisms"
Fournier-Facio, FrancescoBraided 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.