#### Volume 16, issue 6 (2016)

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An invariant of rational homology $3$–spheres via vector fields

### Tatsuro Shimizu

Algebraic & Geometric Topology 16 (2016) 3073–3101
##### Abstract

We give an alternative construction of the Kontsevich–Kuperberg–Thurston invariant for rational homology $3$–spheres. This construction is a generalization of the original construction of the Kontsevich–Kuperberg–Thurston invariant. As an application, we give a Morse homotopy theoretic description of the Kontsevich–Kuperberg–Thurston invariant (close to a description by Watanabe).

##### Keywords
homology 3–sphere, finite type invariant, Chern–Simons perturbation theory, Morse homotopy
Primary: 57M27
##### Publication
Received: 5 November 2013
Revised: 19 March 2016
Accepted: 2 April 2016
Published: 15 December 2016
##### Authors
 Tatsuro Shimizu Research Institute for Mathematical Sciences Kyoto University The Mathematical Society of Japan Kitashirakawa-Oiwake cho Sakyo-ku Kyoto city 606-8502 Japan