This is the calendar of the Illinois' Math Department Topology Seminar. Talks are generally on Tuesdays at 11am, followed by an (optional) lunch with the speaker.
In Fall 2024, the seminar room is Altgeld Hall 241 (unless specified otherwise).
A classical problem in manifold topology is to understand when two given embeddings are isotopic. The desire to understand when such isotopies are unique leads one to instead consider the space of embeddings between two smooth manifolds. Goodwillie and Weiss provide an approach by trying to study the values of embeddings in small neighborhoods of configuration spaces for a manifold. We extend these methods to the setting of manifolds with an action by a finite group. In particular, we study the space of equivariant embeddings by scanning along an appropriate notion of $G$-disks. Leveraging the work of Bierstone in equivariant immersion theory, we show that the first approximation to equivariant embeddings is the space of equivariant immersions. Moreover, we show that the layers of our embedding tower can be analyzed as fibrations over a product of nonequivariant configuration spaces.
Department of Mathematics
College of Liberal Arts & Sciences
273 Altgeld Hall
1409 W. Green Street (MC-382)
Urbana, IL 61801
Telephone: 217-333-3350
Email: math@illinois.edu