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Atlantis Studies in Dynamical Systems

Perturbed Gradient Flow Trees and A∞-algebra Structures in Morse Cohomology

Authors: Mescher, Stephan

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  • Introduces a self-contained discussion of an aspect of Morse theory that has remained largely overlooked
  • Includes an accessible introduction to a part of Morse theory that is closely related to algebraic topology
  • Offers a useful preparation for the study of Fukaya categories in Lagrangian Floer theory
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eBook 53,49 €
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  • ISBN 978-3-319-76584-6
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Hardcover 93,59 €
price for Spain (gross)
  • ISBN 978-3-319-76583-9
  • Free shipping for individuals worldwide
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Softcover 67,59 €
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  • ISBN 978-3-030-09526-0
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  • Institutional customers should get in touch with their account manager
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About this book

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.

About the authors

Dr. Stephan Mescher is a Research Fellow at the University of Leipzig. He graduated with a degree in Mathematics from Bielefeld University in 2008 and obtained his Ph.D. at the University of Leipzig in 2017, supervised by Prof. Matthias Schwarz.

Table of contents (7 chapters)

Table of contents (7 chapters)

Buy this book

eBook 53,49 €
price for Spain (gross)
  • ISBN 978-3-319-76584-6
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 93,59 €
price for Spain (gross)
  • ISBN 978-3-319-76583-9
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 67,59 €
price for Spain (gross)
  • ISBN 978-3-030-09526-0
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Perturbed Gradient Flow Trees and A∞-algebra Structures in Morse Cohomology
Authors
Series Title
Atlantis Studies in Dynamical Systems
Series Volume
6
Copyright
2018
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG, part of Springer Nature
eBook ISBN
978-3-319-76584-6
DOI
10.1007/978-3-319-76584-6
Hardcover ISBN
978-3-319-76583-9
Softcover ISBN
978-3-030-09526-0
Edition Number
1
Number of Pages
XXV, 171
Number of Illustrations
20 b/w illustrations
Topics