Homology, Homotopy and Applications

Higher Morse moduli spaces and $n$-categories

Sonja Hohloch

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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

Permanent link to this document
https://projecteuclid.org/euclid.hha/1408712332

Mathematical Reviews number (MathSciNet)
MR3226919

Zentralblatt MATH identifier
1350.18002

Subjects
Primary: 18B99: None of the above, but in this section 18D99: None of the above, but in this section 55U99: None of the above, but in this section 58E05: Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirel m an) theory, etc.)

Keywords
Morse theory $n$-category theory flow category

Citation

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


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