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SUMMARY:Chain groups of homeomorphisms of the interval and the circle
DTSTART:20160929T130000
DTEND:20160929T140000
DTSTAMP:20260916T074058Z
UID:f9470151a1421e5af2a055c5c8b3990a832f384f8f12035fc2d95599
CATEGORIES:Conferences - Seminars
DESCRIPTION:Yash Lodha (EPFL)\nWe 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\, subje
 ct to a certain mild dynamical condition. The resulting class of groups ex
 hibits a combination of uniformity and diversity. On the one hand\, a chai
 n group either has a simple commutator sub- group or the action of the gro
 up 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 c
 ommutator subgroup. Moreover\, any 2-chain group is isomorphic to Thompson
 ’s group F. On the other hand\, every finitely generated subgroup of Hom
 eo+([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 grou
 p\, as well as uncountably many isomorphism types of countable simple subg
 roups of Homeo+([0\,1]). We also study chain groups of various regularitie
 s\, and show that there are uncountably many isomorphism types of chain gr
 oups which cannot be realized by C2 diffeomorphisms.\nThis is joint work w
 ith Sang-hyun Kim and Thomas Koberda.
LOCATION:MA 31 http://plan.epfl.ch/?room=ma31
STATUS:CONFIRMED
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