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|a 9783319765846
|9 978-3-319-76584-6
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|a 10.1007/978-3-319-76584-6
|2 doi
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|a QA614-614.97
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|a PBKS
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|a 514.74
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|a Mescher, Stephan.
|e author.
|4 aut
|4 http://id.loc.gov/vocabulary/relators/aut
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|a Perturbed Gradient Flow Trees and A∞-algebra Structures in Morse Cohomology
|h [electronic resource] /
|c by Stephan Mescher.
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|a 1st ed. 2018.
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|a Cham :
|b Springer International Publishing :
|b Imprint: Springer,
|c 2018.
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|a XXV, 171 p. 20 illus.
|b online resource.
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|a text
|b txt
|2 rdacontent
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|a computer
|b c
|2 rdamedia
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|a online resource
|b cr
|2 rdacarrier
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|a text file
|b PDF
|2 rda
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|a Atlantis Studies in Dynamical Systems ;
|v 6
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|a 1. Basics on Morse homology -- 2. Perturbations of gradient flow trajectories -- 3. Nonlocal generalizations -- 4. Moduli spaces of perturbed Morse ribbon trees -- 5. The convergence behaviour of sequences of perturbed Morse ribbon trees -- 6. Higher order multiplications and the A∞-relations -- 7. A∞-bimodule structures on Morse chain complexes -- A. Orientations and sign computations for perturbed Morse ribbon trees.
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|a This book elaborates on an idea put forward by M. Abouzaid on equipping the Morse cochain complex of a smooth Morse function on a closed oriented manifold with the structure of an A∞-algebra by means of perturbed gradient flow trajectories. This approach is a variation on K. Fukaya's definition of Morse-A∞-categories for closed oriented manifolds involving families of Morse functions. To make A∞-structures in Morse theory accessible to a broader audience, this book provides a coherent and detailed treatment of Abouzaid's approach, including a discussion of all relevant analytic notions and results, requiring only a basic grasp of Morse theory. In particular, no advanced algebra skills are required, and the perturbation theory for Morse trajectories is completely self-contained. In addition to its relevance for finite-dimensional Morse homology, this book may be used as a preparation for the study of Fukaya categories in symplectic geometry. It will be of interest to researchers in mathematics (geometry and topology), and to graduate students in mathematics with a basic command of the Morse theory.
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|a Global analysis (Mathematics).
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|a Manifolds (Mathematics).
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|a Dynamics.
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|a Ergodic theory.
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|a Complex manifolds.
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|a Global Analysis and Analysis on Manifolds.
|0 http://scigraph.springernature.com/things/product-market-codes/M12082
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|a Dynamical Systems and Ergodic Theory.
|0 http://scigraph.springernature.com/things/product-market-codes/M1204X
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650 |
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|a Manifolds and Cell Complexes (incl. Diff.Topology).
|0 http://scigraph.springernature.com/things/product-market-codes/M28027
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|a SpringerLink (Online service)
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|t Springer eBooks
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|i Printed edition:
|z 9783319765839
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776 |
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|i Printed edition:
|z 9783319765853
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|i Printed edition:
|z 9783030095260
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830 |
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|a Atlantis Studies in Dynamical Systems ;
|v 6
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|u https://doi.org/10.1007/978-3-319-76584-6
|z Full Text via HEAL-Link
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|a ZDB-2-SMA
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|a Mathematics and Statistics (Springer-11649)
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