A morse-bott approach to monopole floer homology and the triangulation conjecture

Francesco Lin

doi:10.1090/memo/1221

A morse-bott approach to monopole floer homology and the triangulation conjecture

Francesco Lin

Mathematics

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18 Scopus citations

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 Pin(2)-equivariant Seiberg-Witten-Floer homology. In particular, we provide an alternative approach to his disproof of the celebrated Triangulation conjecture.

Original language	English (US)
Pages (from-to)	1-174
Number of pages	174
Journal	Memoirs of the American Mathematical Society
Volume	255
Issue number	1221
DOIs	https://doi.org/10.1090/memo/1221
State	Published - Sep 2018

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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10.1090/memo/1221

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AB - 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 spinc structure which is isomorphic to its conjugate, we define the counterpart in this context of Manolescu's recent 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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A morse-bott approach to monopole floer homology and the triangulation conjecture

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