Chain groups of homeomorphisms of the interval and the circle
Event details
| Date | 29.09.2016 |
| Hour | 13:00 › 14:00 |
| Speaker | Yash Lodha (EPFL) |
| Location | |
| Category | Conferences - Seminars |
We introduce the notion of chain groups of homeomorphisms of a one-manifold, which are groups finitely generated by homeomorphisms each sup- ported on exactly one interval in a chain, subject to a certain mild dynamical condition. The resulting class of groups exhibits a combination of uniformity and diversity. On the one hand, a chain group either has a simple commutator sub- group or the action of the group has a wandering interval. In the latter case, the chain group admits a canonical quotient which is also a chain group, and which has a simple commutator subgroup. Moreover, any 2-chain group is isomorphic to Thompson’s group F. On the other hand, every finitely generated subgroup of Homeo+([0,1]) can be realized as a subgroup of a chain group. As a corollary, we show that there are uncountably many isomorphism types of chain group, as well as uncountably many isomorphism types of countable simple subgroups of Homeo+([0,1]). We also study chain groups of various regularities, and show that there are uncountably many isomorphism types of chain groups which cannot be realized by C2 diffeomorphisms.
This is joint work with Sang-hyun Kim and Thomas Koberda.
This is joint work with Sang-hyun Kim and Thomas Koberda.
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- Free