TY  - BOOK
AU  - Lin,Francesco
TI  - A Morse-Bott Approach to Monopole Floer Homology and the Triangulation Conjecture
T2  - Memoirs of the American Mathematical Society Series
SN  - 9781470448196
AV  - QB311 .L56 2018 
U1  - 526.32 
PY  - 2018///
CY  - Providence
PB  - American Mathematical Society
KW  - Triangulation
KW  - Electronic books
N1  - 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
N2  - 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
UR  - https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=5571103
ER  -