A Morse-Bott approach to monopole Floer homology and the Triangulation conjecture

Francesco Lin

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arXiv · 1404.4561

A Morse-Bott approach to monopole Floer homology and the Triangulation conjecture

Francesco Lin

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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 with a spin$^c$ structure 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.

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Francesco Lin. 2015-02-23. A Morse-Bott approach to monopole Floer homology and the Triangulation conjecture. https://arxiv.org/abs/1404.4561

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