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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)
Resource Information
The item Perturbed Gradient Flow Trees and A∞algebra Structures in Morse Cohomology, by Stephan Mescher, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.This item is available to borrow from all library branches.
Resource Information
The item Perturbed Gradient Flow Trees and A∞algebra Structures in Morse Cohomology, by Stephan Mescher, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.
This item is available to borrow from all library branches.
 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 MorseA∞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 selfcontained. In addition to its relevance for finitedimensional 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
 Language
 eng
 Extent
 XXV, 171 p. 20 illus.
 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
 Isbn
 9783319765846
 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
 Subject

 Dynamical Systems and Ergodic Theory
 Dynamics
 Dynamics
 Electronic resources
 Ergodic theory
 Ergodic theory
 Global Analysis and Analysis on Manifolds
 Global analysis (Mathematics)
 Global analysis (Mathematics)
 Manifolds (Mathematics)
 Manifolds (Mathematics)
 Manifolds (Mathematics)
 Manifolds and Cell Complexes (incl. Diff.Topology)
 Mathematics
 Mathematics
 Complex manifolds
 Complex manifolds
 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 MorseA∞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 selfcontained. In addition to its relevance for finitedimensional 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
 http://library.link/vocab/creatorName
 Mescher, Stephan
 Image bit depth
 0
 LC call number
 QA614614.97
 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)
 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
 10.1007/9783319765846
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (DEHe213)9783319765846
 Label
 Perturbed Gradient Flow Trees and A∞algebra Structures in Morse Cohomology, by Stephan Mescher, (electronic resource)
 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
 10.1007/9783319765846
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (DEHe213)9783319765846
Subject
 Dynamical Systems and Ergodic Theory
 Dynamics
 Dynamics
 Electronic resources
 Ergodic theory
 Ergodic theory
 Global Analysis and Analysis on Manifolds
 Global analysis (Mathematics)
 Global analysis (Mathematics)
 Manifolds (Mathematics)
 Manifolds (Mathematics)
 Manifolds (Mathematics)
 Manifolds and Cell Complexes (incl. Diff.Topology)
 Mathematics
 Mathematics
 Complex manifolds
 Complex manifolds
Member of
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