Homology, Homotopy and Applications
Volume 16 (2014)
Higher Morse moduli spaces and $n$-categories
Pages: 1 – 32
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’.
Morse theory, $n$-category theory, flow category
2010 Mathematics Subject Classification
18B99, 18D99, 55U99, 58E05