Homology, Homotopy and Applications

Volume 16 (2014)

Number 2

Higher Morse moduli spaces and $n$-categories

Pages: 1 – 32

DOI: http://dx.doi.org/10.4310/HHA.2014.v16.n2.a1


Sonja Hohloch (Section de Mathématiques, École Polytechnique Fédérale de Lausanne, Switzerland)


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

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Published 30 November 2014