A Morse-Bott approach to monopole Floer homology and the triangulation conjecture / / Francesco Lin
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| Autore: |
Lin Francesco <1988->
|
| Titolo: |
A Morse-Bott approach to monopole Floer homology and the triangulation conjecture / / Francesco Lin
|
| Pubblicazione: | Providence, Rhode Island : , : American Mathematical Society, , [2018] |
| ©2018 | |
| Descrizione fisica: | 1 online resource (174 pages) |
| Disciplina: | 514/.34 |
| Soggetto topico: | Triangulation |
| Manifolds (Mathematics) | |
| Floer homology | |
| Soggetto genere / forma: | Electronic books. |
| Nota di bibliografia: | Includes bibliographical references. |
| Nota di contenuto: | Cover -- Title page -- Chapter 1. Introduction -- Chapter 2. Basic setup -- 2.1. The monopole equations -- 2.2. Blowing up the configuration spaces -- 2.3. Completion and slices -- 2.4. Perturbations -- Chapter 3. The analysis of Morse-Bott singularities -- 3.1. Hessians and Morse-Bott singularities -- 3.2. Moduli spaces of trajectories -- 3.3. Transversality -- 3.4. Compactness and finiteness -- 3.5. Gluing -- 3.6. The moduli space on a cobordism -- Chapter 4. Floer homology for Morse-Bott singularities -- 4.1. Homology of smooth manifolds via stratified spaces -- 4.2. Floer homology -- 4.3. Invariance and functoriality -- Chapter 5. \Pin-monopole Floer homology -- 5.1. An involution in the theory -- 5.2. Equivariant perturbations and Morse-Bott transversality -- 5.3. Invariant chains and Floer homology -- 5.4. Some computations -- 5.5. Manolescu's invariant and the Triangulation conjecture -- Bibliography -- Back Cover. |
| Sommario/riassunto: | 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. |
| Titolo autorizzato: | A Morse-Bott approach to monopole Floer homology and the triangulation conjecture |
| ISBN: | 1-4704-4819-X |
| Formato: | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione: | Inglese |
| Record Nr.: | 9910478891803321 |
| Lo trovi qui: | Univ. Federico II |
| Opac: | Controlla la disponibilità qui |
Serie:
Memoirs of the American Mathematical Society ; ; Volume 255, Number 1221.