Stephan Mescher

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

• Gebundenes Buch

Produktbeschreibung

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 beof interest to researchersin mathematics (geometry and topology), and to graduate students in mathematics with a basic command of the Morse theory.

Produktdetails

• Atlantis Studies in Dynamical Systems 6
• Verlag: Springer / Springer International Publishing / Springer, Berlin
• Artikelnr. des Verlages: 978-3-319-76583-9
• 1st ed. 2018
• Seitenzahl: 200
• Erscheinungstermin: 7. Mai 2018
• Englisch
• Abmessung: 241mm x 160mm x 17mm
• Gewicht: 454g
• ISBN-13: 9783319765839
• ISBN-10: 3319765833
• Artikelnr.: 50820122

Autorenporträt

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.

Inhaltsangabe

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.