Higher Morse moduli spaces and n-categories
arXiv:1703.10696
Abstract
We generalize Cohen & Jones & Segal's flow category whose objects are the critical points of a Morse function and whose morphisms are the Morse moduli spaces between the critical points to an n-category. The n-category construction involves repeatedly doing Morse theory on Morse moduli spaces for which we have to construct a class of suitable Morse functions. It turns out to be an `almost strict' n-category, i.e. it is a strict n-category `up to canonical isomorphisms'.
31 pages, 3 figures, 14 diagrams; In accordance with the journal's copyright, I am making the preprint version of the published paper available on the arXiv