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Bücher Englische Bücher Wissen & Bildung Naturwissenschaft, Medizin, Informatik, Technik Mathematik Geometrie Morse Homology with Differential Graded Coefficients
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Morse Homology with Differential Graded Coefficients
Jean-François Barraud, Mihai Damian, Vincent Humilière, Alexandru Oancea (Gebundene Ausgabe, Englisch)
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Beschreibung
The 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. Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
30.05.2025
Sprache
Englisch
EAN
9783031880193
Herausgeber
Springer International Publishing
Serien- oder Bandtitel
Progress in Mathematics
Sonderedition
Nein
Autor
Jean-François Barraud, Mihai Damian, Vincent Humilière, Alexandru Oancea
Seitenanzahl
229
Einbandart
Gebundene Ausgabe
Schlagwörter
Morse theory, Morse homology, Twisting cocycle, Leray-Serre spectral sequence, Fibrations, Poincaré duality, Floer theory, Floer homotopy theory, Morse homology with DG coefficients
Thema-Inhalt
PBP - Topologie
PBPD - Algebraische Topologie
Höhe
235 mm
Breite
15.5 cm
Hersteller: Springer, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com, Springer Nature Customer Service Center GmbH
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