Cobordism categories and moduli spaces of odd dimensional manifolds

Fabian Hebestreit; Nathan Perlmutter

Cobordism categories and moduli spaces of odd dimensional manifolds

Algebraic Topology 2019-06-25 v4 Geometric Topology

Authors: Fabian Hebestreit , Nathan Perlmutter

Abstract

We prove that the stable moduli space of $(n-1)$ -connected, $n$ -parallelizable, $(2n+1)$ -dimensional manifolds is homology equivalent to an infinite loopspace for $n \geq 4, n \neq 7$ . The main novel ingredient is a version of the cobordism category incorporating surgery data in the form of Lagrangian subspaces.

Keywords

cobordism categories moduli spaces odd dimensional manifolds surgery data Lagrangian subspaces infinite loopspace

Cite

@article{arxiv.1606.06168,
  title  = {Cobordism categories and moduli spaces of odd dimensional manifolds},
  author = {Fabian Hebestreit and Nathan Perlmutter},
  journal= {arXiv preprint arXiv:1606.06168},
  year   = {2019}
}

Comments

57 pages. Minor revision, to appear in Advances in Mathematics

Cobordism categories and moduli spaces of odd dimensional manifolds

Abstract

Keywords

Cite

Comments

Related papers