Perturbed Gradient Flow Trees and A?-algebra Structures in Morse Cohomology (eBook)

Stephan Mescher (Autor)

eBook Download: PDF

2018 | 1. Auflage
171 Seiten
Springer-Verlag
9783319765846 (ISBN)

Infos

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.

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.

Produkt-Details

• Erscheint lt. Verlag: 25.4.2018
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• ISBN-13: 9783319765846 / 9783319765846