{"product_id":"9783031880223","title":"Morse Homology with Differential Graded Coefficients","description":"\u003ch3\u003eProgress in Mathematics\u003c\/h3\u003e\u003ch1\u003eMorse Homology with Differential Graded Coefficients\u003c\/h1\u003e\u003ch3\u003eJean-François Barraud | Mihai Damian | Vincent Humilière | Alexandru Oancea\u003c\/h3\u003e\u003cdiv\u003e\u003cb\u003eMathematics \/ Topology\u003c\/b\u003e\u003c\/div\u003e\u003cbr\u003e\u003cdiv\u003e\n\u003cp\u003eThe 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. \u003c\/p\u003e\r\n\u003cp\u003eThe 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. \u003c\/p\u003e\r\n\u003cp\u003eThe 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. \u003c\/p\u003e\n\u003c\/div\u003e\u003cdiv\u003e\n\u003cp\u003eJean-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.\u003c\/p\u003e\r\n\u003cp\u003eMihai 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.\u003c\/p\u003e\r\n\u003cp\u003eVincent Humilière is professor of mathematics at Sorbonne Université. His research interests are centered on symplectic topology and its applications to dynamics. \u003c\/p\u003e\r\n\u003cp\u003eAlexandru 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.\u003c\/p\u003e\n\u003c\/div\u003e\u003cbr\u003e\u003ctable\u003e\n\u003ctr\u003e\n\u003ctd\u003ePublication Date: \u003c\/td\u003e\n\u003ctd\u003e30 May 2026\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003ePublisher: \u003c\/td\u003e\n\u003ctd\u003eSpringer Nature Switzerland\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eImprint: \u003c\/td\u003e\n\u003ctd\u003eBirkhäuser\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eISBN-13: \u003c\/td\u003e\n\u003ctd\u003e9783031880223\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eFormat: \u003c\/td\u003e\n\u003ctd\u003ePaperback \/ softback\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003ePage Count: \u003c\/td\u003e\n\u003ctd\u003e229\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003c\/table\u003e","brand":"Springer Nature Switzerland","offers":[{"title":"Default Title","offer_id":51030614900876,"sku":"9783031880223","price":152.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783031880223.jpg?v=1782479555","url":"https:\/\/lateknightbooks.com\/products\/9783031880223","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}