Veranstaltungen

In this first out of three talks, we will explain in detail the transverse spheres lemma by Quinn, which is the key geometric result that allows for the separation of infinitely many locally finite immersed 2-discs in a non-compact 4-manifold. The phenomena coming out of this lemma also allow one to understand why Quinn’s proof of this separation of infinite data is as complex as it is. We will explain these phenomena for future reference.

Bökstedt periodicity refers to Bökstedt's seminal description of topological Hochschild homology of finite fields. I will discuss a recent project with T. Nikolaus on computations of THH based on a relative version of Bökstedt periodicity. Our main applications are quotients of discrete valuation rings, generalizing Brun’s results for Z/p^n.

We study the homology of Riemannian manifolds of finite volume that are covered by a product of r copies  of the hyperbolic plane. Using a variation of a method developed by Avramidi and Nyguen-Phan, we show that any such manifold  M possesses, up to finite coverings, an arbitrarily large number of compact oriented flat totally geodesic r-dimensional submanifolds whose fundamental classes are linearly independent in the r-th homology group of M.