Logic & Set Theory seminar: Classifiability of Homeomorphism Relations
Vadim Kulikov,University of Helsinki
Howard House, 4th floor seminar room
We look at the descriptive complexity of the homeomorphism relation (h.r.) on various subclasses of Polish spaces. One special case are the compact connected three dimensional manifolds whose classification up to h.r. was the subject of the Poincare conjecture. We look at the question of non-compact manifolds, compact and locally compact Polish spaces and a class of Polish spaces consisting of those subsets of R^3 which are the union of an open set and a singleton. We will describe known results proved by Kechris, Solecki that compact Polish h.r. is below a Polish group action, Zielinski and Sabok that it is exactly Polish group action, we will extend this to locally compact spaces and finally show that once local compactness breaks down minimally (just in one point) we lose that and the h.r. is not reducible to an equivalence relation induced by a Polish group action.
Organiser: Andrew Brooke-Taylor Philip Welch Please note this Seminar sarts at 14.00