LEADER 03093nam 2200481 450 001 9910793296303321 005 20220528000051.0 010 $a1-4704-4819-X 035 $a(CKB)4100000007133850 035 $a(MiAaPQ)EBC5571103 035 $a(Au-PeEL)EBL5571103 035 $a(OCoLC)1042567976 035 $a(RPAM)20701218 035 $a(PPN)231946198 035 $a(EXLCZ)994100000007133850 100 $a20220528d2018 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 12$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. 517 3 $aMorse Bott approach to monopole Floer homology and the triangulation conjecture 606 $aTriangulation 615 0$aTriangulation. 676 $a526.32 700 $aLin$b Francesco$f1988-$01544049 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910793296303321 996 $aA Morse-Bott approach to monopole Floer homology and the triangulation conjecture$93797933 997 $aUNINA