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

In the present work the author generalizes 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 {\rm spin}^c structure which is isomorphic...

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Detalles Bibliográficos
Autor principal: Lin, Francesco
Lenguaje:eng
Publicado: American Mathematical Society 2018
Materias:
Mathematical Physics and Mathematics
Acceso en línea:http://cds.cern.ch/record/2653925
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author Lin, Francesco
author_facet Lin, Francesco
author_sort Lin, Francesco
collection CERN
description In the present work the author generalizes 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 {\rm spin}^c structure which is isomorphic to its conjugate, the author defines the counterpart in this context of Manolescu's recent Pin(2)-equivariant Seiberg-Witten-Floer homology. In particular, the author provides an alternative approach to his disproof of the celebrated Triangulation conjecture.
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institution Organización Europea para la Investigación Nuclear
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publishDate 2018
publisher American Mathematical Society
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spelling cern-26539252021-04-21T18:37:08Zhttp://cds.cern.ch/record/2653925engLin, FrancescoA Morse-Bott approach to monopole Floer homology and the triangulation conjectureMathematical Physics and MathematicsIn the present work the author generalizes 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 {\rm spin}^c structure which is isomorphic to its conjugate, the author defines the counterpart in this context of Manolescu's recent Pin(2)-equivariant Seiberg-Witten-Floer homology. In particular, the author provides an alternative approach to his disproof of the celebrated Triangulation conjecture.American Mathematical Societyoai:cds.cern.ch:26539252018
spellingShingle Mathematical Physics and Mathematics
Lin, Francesco
A Morse-Bott approach to monopole Floer homology and the triangulation conjecture
title A Morse-Bott approach to monopole Floer homology and the triangulation conjecture
title_full A Morse-Bott approach to monopole Floer homology and the triangulation conjecture
title_fullStr A Morse-Bott approach to monopole Floer homology and the triangulation conjecture
title_full_unstemmed A Morse-Bott approach to monopole Floer homology and the triangulation conjecture
title_short A Morse-Bott approach to monopole Floer homology and the triangulation conjecture
title_sort morse-bott approach to monopole floer homology and the triangulation conjecture
topic Mathematical Physics and Mathematics
url http://cds.cern.ch/record/2653925
work_keys_str_mv AT linfrancesco amorsebottapproachtomonopolefloerhomologyandthetriangulationconjecture
AT linfrancesco morsebottapproachtomonopolefloerhomologyandthetriangulationconjecture

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