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Logic Seminar

Monday, April 5, 2021
12:00pm to 1:00pm
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Subgroups of PLo(I)PLo^fo(I) which do not embed into Thompson's group FF
Justin Moore, Department of Mathematics, Cornell University,

The group PLo(I)PLofo⁡(I) of piecewise linear orientation preserving homeomorphisms of the unit interval, equipped with composition, has a rich array of finitely generated subgroups. A basic question one can ask is when one of these groups embeds into another. One group which seems to play a particularly important role in this quasi-order is Richard Thompson's group FF. For instance it is conjectured that every finitely generated subgroup of PLo(I)PLo⁡fo(I) either contains a copy of FF or else embeds into FF. I will describe a general dynamical criterion for when a subgroup of PLo(I)PLofo⁡(I) does not embed into FF which covers all known examples. This is joint work with James Hyde.

For more information, please email A. Kechris at [email protected].