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A Morse-Bott Approach to Monopole Floer Homology and the Triangulation Conjecture


About this Title

Francesco Lin

Publication: Memoirs of the American Mathematical Society
Publication Year: 2018; Volume 255, Number 1221
ISBNs: 978-1-4704-2963-8 (print); 978-1-4704-4819-6 (online)
DOI: https://doi.org/10.1090/memo/1221
Published electronically: June 26, 2018

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Table of Contents


Chapters

  • Chapter 1. Introduction
  • Chapter 2. Basic setup
  • Chapter 3. The analysis of Morse-Bott singularities
  • Chapter 4. Floer homology for Morse-Bott singularities
  • Chapter 5. $\mathrm Pin(2)$-monopole Floer homology

Abstract


In the present work we generalize the construction of monopole Floer homology due to Kronheimer and Mrowka to the case of a gradient flow with Morse-Bott singularities. Focusing then on the special case of a three-manifold equipped equipped with a spin structure which is isomorphic to its conjugate, we define the counterpart in this context of Manolescu's recent -equivariant Seiberg-Witten-Floer homology. In particular, we provide an alternative approach to his disproof of the celebrated Triangulation conjecture.

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