Professor Gao invites you to attend the PhD dissertation defense of Michael Cotton

"Abelian group actions and hypersmooth eqivalence relations"

Abstract:

We generalize a result of Gao and Jackson which says that a Borel action of a countable abelian group induces an orbit equivalence relation which is hyperfinite, i.e., reducible to one induced by a Borel ℤ-action. We show that marker sets may still be constructed for any Borel action of a locally compact group, provide definable constructions of appropriate bases for the stabilizers of the acting group, and apply a slight adaptation the Gao-Jackson orthogonal markers machinery to conclude that a Borel action of a group which is isomorphic to the sum of a countable abelian group with a countable sum of copies of ℝ and ℝ/ℤ induces an orbit equivalence relation which is hypersmooth. It also follows that a Borel action of a second countable locally compact abelian group induces an equivalence relation which is still reducible to a Borel ℤ-action.

Cake and coffee will be served in GAB 472 following the event.