LEADER 04913nam 22006735 450 001 9910865256703321 005 20251215153357.0 010 $a9789819717989$b(electronic bk.) 010 $z9789819717972 024 7 $a10.1007/978-981-97-1798-9 035 $a(MiAaPQ)EBC31458829 035 $a(Au-PeEL)EBL31458829 035 $a(CKB)32249732900041 035 $a(MiAaPQ)EBC31461399 035 $a(Au-PeEL)EBL31461399 035 $a(DE-He213)978-981-97-1798-9 035 $a(EXLCZ)9932249732900041 100 $a20240606d2024 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aLagrangian Floer Theory and Its Deformations $eAn Introduction to Filtered Fukaya Category /$fby Yong-Geun Oh 205 $a1st ed. 2024. 210 1$aSingapore :$cSpringer Nature Singapore :$cImprint: Springer,$d2024. 215 $a1 online resource (426 pages) 225 1 $aKIAS Springer Series in Mathematics,$x2731-5150 ;$v2 311 08$aPrint version: Oh, Yong-Geun Lagrangian Floer Theory and Its Deformations Singapore : Springer,c2024 9789819717972 327 $aBased Loop Space and A? Space -- A? Algebras and Modules: Unfiltered Case -- Obstruction-Deformation Theory of Filtered A? Bimodules -- Symplectic Geometry and Hamiltonian Dynamics -- Analysis of Pseudoholomorphic Curves and Bordered Stable Maps -- Critical Points of Potential Functions and Floer Cohomology -- Filtered Fukaya Category and its Bulk Deformations. 330 $aA-infinity structure was introduced by Stasheff in the 1960s in his homotopy characterization of based loop space, which was the culmination of earlier works of Sugawara's homotopy characterization of H-spaces and loop spaces. At the beginning of the 1990s, a similar structure was introduced by Fukaya in his categorification of Floer homology in symplectic topology. This structure plays a fundamental role in the celebrated homological mirror symmetry proposal by Kontsevich and in more recent developments of symplectic topology. A detailed construction of A-infinity algebra structure attached to a closed Lagrangian submanifold is given in Fukaya, Oh, Ohta, and Ono's two-volume monograph Lagrangian Intersection Floer Theory (AMS-IP series 46 I & II), using the theory of Kuranishi structures?a theory that has been regarded as being not easily accessible to researchers in general. The present lecture note is provided by one of the main contributors to the Lagrangian Floer theory and is intended to provide a quick, reader-friendly explanation of the geometric part of the construction. Discussion of the Kuranishi structures is minimized, with more focus on the calculations and applications emphasizing the relevant homological algebra in the filtered context. The book starts with a quick explanation of Stasheff polytopes and their two realizations?one by the rooted metric ribbon trees and the other by the genus-zero moduli space of open Riemann surfaces?and an explanation of the A-infinity structure on the motivating example of the based loop space. It then provides a description of the moduli space of genus-zero bordered stable maps and continues with the construction of the (curved) A-infinity structure and its canonical models. Included in the explanation are the (Landau?Ginzburg) potential functions associated with compact Lagrangian submanifolds constructed by Fukaya, Oh, Ohta, and Ono. The book explains calculations of potential functions for toric fibers in detail and reviews several explicit calculations in the literature of potential functions with bulk as well as their applications to problems in symplectic topology via the critical point theory thereof. In the Appendix, the book also provides rapid summaries of various background materials such as the stable map topology, Kuranishi structures, and orbifold Lagrangian Floer theory. 410 0$aKIAS Springer Series in Mathematics,$x2731-5150 ;$v2 606 $aGeometry, Differential 606 $aAlgebraic topology 606 $aTopology 606 $aDifferential Geometry 606 $aAlgebraic Topology 606 $aTopology 606 $aEspais de llaços$2thub 606 $aFuncions de Lagrange$2thub 606 $aHomologia$2thub 608 $aLlibres electrònics$2thub 615 0$aGeometry, Differential. 615 0$aAlgebraic topology. 615 0$aTopology. 615 14$aDifferential Geometry. 615 24$aAlgebraic Topology. 615 24$aTopology. 615 7$aEspais de llaços 615 7$aFuncions de Lagrange 615 7$aHomologia 676 $a516.36 700 $aOh$b Yong-Geun$0732183 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9910865256703321 996 $aLagrangian Floer Theory and Its Deformations$94168711 997 $aUNINA