## Homology, Homotopy and Applications

### Higher Morse moduli spaces and $n$-categories

Sonja Hohloch

#### 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'.

#### Article information

Source
Homology Homotopy Appl., Volume 16, Number 2 (2014), 1-32.

Dates
First available in Project Euclid: 22 August 2014

Hohloch, Sonja. Higher Morse moduli spaces and $n$-categories. Homology Homotopy Appl. 16 (2014), no. 2, 1--32. https://projecteuclid.org/euclid.hha/1408712332