FSU-UF Topology Meeting

Title: Equivariant subsets of Peano continuua under p-adic actions

Speaker: James Maissen (University of Florida)

Abstract: The Hilbert-Smith conjecture asks if a p-adic group can act effectively upon a manifold. It was recently shown to hold true for manifolds of dimension 3. With the conjecture in mind, I investigate a slightly larger category of spaces: Peano continua. I prove that every effective p-adic action on a peano continuum admits an equivariant partitioning. I show how to lift arcs and other simply connected continua from the quotient spaces of these actions. Finally, in the specific case of a free action on a sub-collection of Peano continua that include higher dimensional manifolds, I show that for every point in the space one can find a number of interesting equivariant sub-continua which include any number of p-adic solenoids and the 1-dimensional menger curve.