Algebra/Topology seminar

Speaker: Michael Weiss

Title: Spaces of topological embeddings in codimension at least 3

Abstract: This is about joint work with P Boavida de Brito concerning mainly the space of topological embeddings of R^m in R^n where n-m is at least 3 and n is at least 5. The main theorem (proof nearly finished) is that the space of these embeddings is weakly homotopy equivalent to the space of derived maps from the operad of little m-disks to the operad of little n-disks. There is a more precise although less striking formulation in which the operads are replaced by the "configuration categories" of R^m and R^n, respectively. --The m times looped version of this statement has been known for some time (at least 5 yrs), so that the challenge consists mainly in delooping some known theories and points of view. For that we use a torus trick. 

There is also a version of the statement for topological embeddings of M in N, where M and N are arbitrary topological manifolds (codimension at least 3). Most of this can be deduced from the special case M= R^m and N=R^n using some formal arguments and/or well-known theorems.