03093nam 2200481 450 991079329630332120220528000051.01-4704-4819-X(CKB)4100000007133850(MiAaPQ)EBC5571103(Au-PeEL)EBL5571103(OCoLC)1042567976(RPAM)20701218(PPN)231946198(EXLCZ)99410000000713385020220528d2018 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierA Morse-Bott approach to monopole Floer homology and the triangulation conjecture /Francesco LinProvidence, Rhode Island :American Mathematical Society,[2018]©20181 online resource (174 pages)Memoirs of the American Mathematical Society ;Volume 255, Number 12211-4704-2963-2 Includes bibliographical references.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.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.Memoirs of the American Mathematical Society ;Volume 255, Number 1221.Morse Bott approach to monopole Floer homology and the triangulation conjectureTriangulationTriangulation.526.32Lin Francesco1988-1544049MiAaPQMiAaPQMiAaPQBOOK9910793296303321A Morse-Bott approach to monopole Floer homology and the triangulation conjecture3797933UNINA