Erschienen: 01.02.2018 Abbildung von Mescher | Perturbed Gradient Flow Trees and A8-algebra Structures in Morse Cohomology | 1st ed. 2018 | 2018

Mescher

Perturbed Gradient Flow Trees and A8-algebra Structures in Morse Cohomology

lieferbar ca. 10 Tage als Sonderdruck ohne Rückgaberecht

auch verfügbar als eBook (PDF) für 82.38 €

1st ed. 2018 2018. Buch. 200 S. HC runder Rücken kaschiert. Hardcover

Springer International Publishing. ISBN 978-3-319-76583-9

Format (B x L): 15.9 x 24.1 cm

Gewicht: 456 g

In englischer Sprache

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 A8-algebra by means of perturbed gradient flow trajectories. This approach is a variation on K. Fukaya's definition of Morse-A8-categories for closed oriented manifolds involving families of Morse functions. To make A8-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.

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