Higher Morse moduli spaces and n-categoriesHigher Morse moduli spaces and n-categories
Faculty of Sciences. Mathematics and Computer Science
Homology, homotopy & applications
16(2014):2, p. 1-32
We generalize Cohen & Jones & Segal's ow 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'.