Algebra/Topology seminar

Speaker: Boris Botvinnik (University of Oregon, USA)

Title: Stable moduli spaces of high dimensional handlebodies

Abstract: I will report on a recent joint work with Nathan Perlmutter.
We study the moduli space of handlebodies, i.e. the classifying space
$\BDiff((D^{n+1}\times S^n)^{\natural g}, D^{2n})$ of the group of
  diffeomorphisms that restrict to the identity near an embedded
disk $D^{2n} \subset \partial (D^{n+1}\times S^n)^{\natural g}$.
We prove that there is a natural map
$$\colim_{g\to\infty}\BDiff((D^{n+1}\times
S^n)^{\natural g}, D^{2n}) \;
\longrightarrow \; Q_{0}BO(2n+1)\langle n \rangle_{+}
$$
which induces an isomorphism in integral homology when $n\geq 4$. Above,
$BO(2n+1)\langle n \rangle$ denotes the $n$-connective cover of
$BO(2n+1)$.