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200 12$aA Morse-Bott approach to monopole Floer homology and the triangulation conjecture /$fFrancesco Lin
210  1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d[2018]
210  4$dİ2018
215   $a1 online resource (174 pages)
225 1 $aMemoirs of the American Mathematical Society ;$vVolume 255, Number 1221
311   $a1-4704-2963-2 
320   $aIncludes bibliographical references.
327   $aCover -- 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.
330   $aIn the present work the author generalizes the construction of monopole Floer homology due to Kronheimer and Mrowka to the case of a gradient flow with Morse-Bott singularities. Focusing then on the special case of a three-manifold equipped equipped with a {\rm spin}^c structure which is isomorphic to its conjugate, the author defines the counterpart in this context of Manolescu's recent Pin(2)-equivariant Seiberg-Witten-Floer homology. In particular, the author provides an alternative approach to his disproof of the celebrated Triangulation conjecture.
410  0$aMemoirs of the American Mathematical Society ;$vVolume 255, Number 1221.
606   $aTriangulation
606   $aManifolds (Mathematics)
606   $aFloer homology
608   $aElectronic books.
615  0$aTriangulation.
615  0$aManifolds (Mathematics)
615  0$aFloer homology.
676   $a514/.34
700   $aLin$b Francesco$f1988-$01046835
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910478891803321
996   $aA Morse-Bott approach to monopole Floer homology and the triangulation conjecture$92474058
997   $aUNINA