LEADER 00750nam0-22002651i-450- 001 990004916320403321 005 19990530 035 $a000491632 035 $aFED01000491632 035 $a(Aleph)000491632FED01 035 $a000491632 100 $a19990530g19729999km-y0itay50------ba 101 0 $aita 105 $ay-------001yy 200 1 $aPoètique des Liaisons Dangereuses$fChristine Belcikowski 210 $aParis$cLibrairie JosT Corti$d1972. 215 $a188 p.$d23 cm 700 1$aBelcikowski,$bChristine$0197126 801 0$aIT$bUNINA$gRICA$2UNIMARC 901 $aBK 912 $a990004916320403321 952 $aSH 383$bFil. Mod. 22054$fFLFBC 959 $aFLFBC 996 $aPoètique des Liaisons Dangereuses$9525441 997 $aUNINA LEADER 04217nam 22005535 450 001 9911007359003321 005 20250530130703.0 010 $a3-031-88020-X 024 7 $a10.1007/978-3-031-88020-9 035 $a(CKB)39124444300041 035 $a(MiAaPQ)EBC32141288 035 $a(Au-PeEL)EBL32141288 035 $a(DE-He213)978-3-031-88020-9 035 $a(EXLCZ)9939124444300041 100 $a20250530d2025 u| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aMorse Homology with Differential Graded Coefficients /$fby Jean-François Barraud, Mihai Damian, Vincent Humilière, Alexandru Oancea 205 $a1st ed. 2025. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Birkhäuser,$d2025. 215 $a1 online resource (231 pages) 225 1 $aProgress in Mathematics,$x2296-505X ;$v360 311 08$a3-031-88019-6 327 $aIntroduction and Main Results -- Morse vs DG Morse Homology Toolset -- Comparison of the Barraud-Cornea Cocycle and the Brown Cocycle -- Algebraic Properties of Twisted Complexes -- Morse Homology with DG-Coefficients: Construction -- Morse Homology with DG-Coefficients: Invariance -- Fibrations -- Functoriality: General Properties -- Functoriality: First Definition -- Functoriality: Second Definition. Cohomology and Poincaré Duality -- Shriek Maps and Poincaré Duality for Non-Orientable Manifolds -- Beyond the Case of Manifolds of Finite Dimension -- Appendix: Comparison of Geometry and Analytic Orientations in Morse Theory. 330 $aThe key geometric objects underlying Morse homology are the moduli spaces of connecting gradient trajectories between critical points of a Morse function. The basic question in this context is the following: How much of the topology of the underlying manifold is visible using moduli spaces of connecting trajectories? The answer provided by ?classical? Morse homology as developed over the last 35 years is that the moduli spaces of isolated connecting gradient trajectories recover the chain homotopy type of the singular chain complex. The purpose of this monograph is to extend this further: the fundamental classes of the compactified moduli spaces of connecting gradient trajectories allow the construction of a twisting cocycle akin to Brown?s universal twisting cocycle. As a consequence, the authors define (and compute) Morse homology with coefficients in any differential graded (DG) local system. As particular cases of their construction, they retrieve the singular homology of the total space of Hurewicz fibrations and the usual (Morse) homology with local coefficients. A full theory of Morse homology with DG coefficients is developed, featuring continuation maps, invariance, functoriality, and duality. Beyond applications to topology, this is intended to serve as a blueprint for analogous constructions in Floer theory. The new material and methods presented in the text will be of interest to a broad range of researchers in topology and symplectic topology. At the same time, the authors are particularly careful to give gentle introductions to the main topics and have structured the text so that it can be easily read at various degrees of detail. As such, the book should already be accessible and of interest to graduate students with a general interest in algebra and topology. . 410 0$aProgress in Mathematics,$x2296-505X ;$v360 606 $aManifolds (Mathematics) 606 $aAlgebraic topology 606 $aManifolds and Cell Complexes 606 $aAlgebraic Topology 615 0$aManifolds (Mathematics) 615 0$aAlgebraic topology. 615 14$aManifolds and Cell Complexes. 615 24$aAlgebraic Topology. 676 $a514.34 700 $aBarraud$b Jean-François$01823673 701 $aDamian$b Mihai$0524784 701 $aHumilière$b Vincent$01823674 701 $aOancea$b Alexandru$01823675 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9911007359003321 996 $aMorse Homology with Differential Graded Coefficients$94390487 997 $aUNINA