The Resource Perturbed Gradient Flow Trees and A∞-algebra Structures in Morse Cohomology, by Stephan Mescher, (electronic resource)

Perturbed Gradient Flow Trees and A∞-algebra Structures in Morse Cohomology, by Stephan Mescher, (electronic resource)

Label
Perturbed Gradient Flow Trees and A∞-algebra Structures in Morse Cohomology
Title
Perturbed Gradient Flow Trees and A∞-algebra Structures in Morse Cohomology
Statement of responsibility
by Stephan Mescher
Creator
Contributor
Author
Provider
Subject
Language
eng
Summary
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
Member of
http://library.link/vocab/creatorName
Mescher, Stephan
Image bit depth
0
LC call number
QA614-614.97
Literary form
non fiction
http://library.link/vocab/relatedWorkOrContributorName
SpringerLink
Series statement
Atlantis Studies in Dynamical Systems
Series volume
6
http://library.link/vocab/subjectName
  • Mathematics
  • Dynamics
  • Ergodic theory
  • Global analysis (Mathematics)
  • Manifolds (Mathematics)
  • Complex manifolds
  • Mathematics
  • Global Analysis and Analysis on Manifolds
  • Dynamical Systems and Ergodic Theory
  • Manifolds and Cell Complexes (incl. Diff.Topology)
Label
Perturbed Gradient Flow Trees and A∞-algebra Structures in Morse Cohomology, by Stephan Mescher, (electronic resource)
Instantiates
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
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
Dimensions
unknown
Extent
XXV, 171 p. 20 illus.
File format
multiple file formats
Form of item
electronic
Isbn
9783319765846
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-319-76584-6
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-3-319-76584-6
Label
Perturbed Gradient Flow Trees and A∞-algebra Structures in Morse Cohomology, by Stephan Mescher, (electronic resource)
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
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
Dimensions
unknown
Extent
XXV, 171 p. 20 illus.
File format
multiple file formats
Form of item
electronic
Isbn
9783319765846
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-319-76584-6
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-3-319-76584-6

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