LEADER 03724nam 22006255 450 001 9910513578303321 005 20240214155116.0 010 $a981-16-7838-3 024 7 $a10.1007/978-981-16-7838-7 035 $a(MiAaPQ)EBC6827721 035 $a(Au-PeEL)EBL6827721 035 $a(CKB)20151344300041 035 $a(OCoLC)1290022695 035 $a(DE-He213)978-981-16-7838-7 035 $a(PPN)259387509 035 $a(EXLCZ)9920151344300041 100 $a20211215d2021 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aRecent Progress on the Donaldson?Thomas Theory $eWall-Crossing and Refined Invariants /$fby Yukinobu Toda 205 $a1st ed. 2021. 210 1$aSingapore :$cSpringer Nature Singapore :$cImprint: Springer,$d2021. 215 $a1 online resource (110 pages) 225 1 $aSpringerBriefs in Mathematical Physics,$x2197-1765 ;$v43 311 08$aPrint version: Toda, Yukinobu Recent Progress on the Donaldson-Thomas Theory Singapore : Springer Singapore Pte. Limited,c2022 9789811678370 327 $a1Donaldson?Thomas invariants on Calabi?Yau 3-folds -- 2Generalized Donaldson?Thomas invariants -- 3Donaldson?Thomas invariants for quivers with super-potentials -- 4Donaldson?Thomas invariants for Bridgeland semistable objects -- 5Wall-crossing formulas of Donaldson?Thomas invariants -- 6Cohomological Donaldson?Thomas invariants -- 7Gopakumar?Vafa invariants -- 8Some future directions. 330 $aThis book is an exposition of recent progress on the Donaldson?Thomas (DT) theory. The DT invariant was introduced by R. Thomas in 1998 as a virtual counting of stable coherent sheaves on Calabi?Yau 3-folds. Later, it turned out that the DT invariants have many interesting properties and appear in several contexts such as the Gromov?Witten/Donaldson?Thomas conjecture on curve-counting theories, wall-crossing in derived categories with respect to Bridgeland stability conditions, BPS state counting in string theory, and others. Recently, a deeper structure of the moduli spaces of coherent sheaves on Calabi?Yau 3-folds was found through derived algebraic geometry. These moduli spaces admit shifted symplectic structures and the associated d-critical structures, which lead to refined versions of DT invariants such as cohomological DT invariants. The idea of cohomological DT invariants led to a mathematical definition of the Gopakumar?Vafa invariant, which was first proposed by Gopakumar?Vafa in 1998, but its precise mathematical definition has not been available until recently. This book surveys the recent progress on DT invariants and related topics, with a focus on applications to curve-counting theories. 410 0$aSpringerBriefs in Mathematical Physics,$x2197-1765 ;$v43 606 $aMathematical physics 606 $aGeometry, Algebraic 606 $aAlgebra, Homological 606 $aMathematical Physics 606 $aAlgebraic Geometry 606 $aCategory Theory, Homological Algebra 606 $aInvariants$2thub 608 $aLlibres electrònics$2thub 615 0$aMathematical physics. 615 0$aGeometry, Algebraic. 615 0$aAlgebra, Homological. 615 14$aMathematical Physics. 615 24$aAlgebraic Geometry. 615 24$aCategory Theory, Homological Algebra. 615 7$aInvariants 676 $a512.55 700 $aToda$b Yukinobu$01071417 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910513578303321 996 $aRecent Progress on the Donaldson?Thomas Theory$93562081 997 $aUNINA