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

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...

Πλήρης περιγραφή

Λεπτομέρειες βιβλιογραφικής εγγραφής
Κύριος συγγραφέας: Mescher, Stephan (Συγγραφέας, http://id.loc.gov/vocabulary/relators/aut)
Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
Γλώσσα:English
Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2018.
Έκδοση:1st ed. 2018.
Σειρά:Atlantis Studies in Dynamical Systems ; 6
Θέματα:
Διαθέσιμο Online:Full Text via HEAL-Link
Πίνακας περιεχομένων:
  • 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.