Geodesic
Higher Morse moduli spaces and $n$-categories
Homology, homotopy, and applications, Tome 16 (2014) no. 2, pp. 1-32.

Voir la notice de l'article provenant de la source International Press of Boston

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’.
DOI : 10.4310/HHA.2014.v16.n2.a1
Classification : 18B99, 18D99, 55U99, 58E05
Keywords: Morse theory, $n$-category theory, flow category 
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Sonja Hohloch. Higher Morse moduli spaces and $n$-categories. Homology, homotopy, and applications, Tome 16 (2014) no. 2, pp. 1-32. doi : 10.4310/HHA.2014.v16.n2.a1. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2014.v16.n2.a1/

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