LEADER 03144nam 2200517 450 001 9910478891803321 005 20211029210852.0 010 $a1-4704-4819-X 035 $a(CKB)4100000007133850 035 $a(MiAaPQ)EBC5571103 035 $a(PPN)231946198 035 $a(Au-PeEL)EBL5571103 035 $a(OCoLC)1042567976 035 $a(EXLCZ)994100000007133850 100 $a20181203d2018 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. 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 LEADER 01567oam 2200469zu 450 001 9910146770703321 005 20241212215306.0 010 $a9781509096725 010 $a1509096728 035 $a(CKB)1000000000022697 035 $a(SSID)ssj0000395964 035 $a(PQKBManifestationID)12119829 035 $a(PQKBTitleCode)TC0000395964 035 $a(PQKBWorkID)10460291 035 $a(PQKB)10237075 035 $a(EXLCZ)991000000000022697 100 $a20160829d2005 uy 101 0 $aeng 181 $ctxt 182 $cc 183 $acr 200 10$a2005 International Quantum Electronics Conference (IQEC) : Tokyo, Japan, 11-15 July, 2005 210 31$a[Place of publication not identified]$cInstitute of Electrical and Electronics Engineers$d2005 300 $aBibliographic Level Mode of Issuance: Monograph 311 08$a9780780392403 311 08$a078039240X 606 $aQuantum electronics$vCongresses 606 $aPhysics$2HILCC 606 $aPhysical Sciences & Mathematics$2HILCC 606 $aElectricity & Magnetism$2HILCC 615 0$aQuantum electronics 615 7$aPhysics 615 7$aPhysical Sciences & Mathematics 615 7$aElectricity & Magnetism 676 $a537.5 712 02$aInstitute of Electrical and Electronics Engineers 712 12$aInternational Quantum Electronics Conference 801 0$bPQKB 906 $aPROCEEDING 912 $a9910146770703321 996 $a2005 International Quantum Electronics Conference (IQEC) : Tokyo, Japan, 11-15 July, 2005$92522333 997 $aUNINA