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A Morse-Bott Approach to Monopole Floer Homology and the Triangulation Conjecture
About this Title
Francesco Lin, Department of Mathematics, Massachusetts Institute of Technology
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
MSC: Primary 57M27, 57R58
Table of Contents
Chapters
- 1. Introduction
- 2. Basic setup
- 3. The analysis of Morse-Bott singularities
- 4. Floer homology for Morse-Bott singularities
- 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$^c$ structure which is isomorphic to its conjugate, we define the counterpart in this context of Manolescu’s recent $\mathrm {Pin}(2)$-equivariant Seiberg-Witten-Floer homology. In particular, we provide an alternative approach to his disproof of the celebrated Triangulation conjecture.- D. M. Austin and P. J. Braam, Morse-Bott theory and equivariant cohomology, The Floer memorial volume, Progr. Math., vol. 133, Birkhäuser, Basel, 1995, pp. 123–183. MR 1362827
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