Morse Homology with Differential Graded Coefficients

Jean-François Barraud is professor of mathematics at the University of Toulouse. His research focuses on symplectic topology, with a predilection for Morse, stable Morse and Floer theory.Mihai Damian is a mathematician working in differential and symplectic topology, and more specifically in Morse and Floer theory. He is the author of several research papers and a book on these topics. He is currently associate professor at the University of Strasbourg.Vincent Humilière is professor of mathematics at Sorbonne Université. His research interests are centered on symplectic topology and its applications to dynamics. Alexandru Oancea is a mathematician doing research in symplectic topology, with a special interest in string topology, Hamiltonian dynamics, and algebraic topology. He is currently professor of mathematics at the University of Strasbourg.

• Introduction 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.