Title: Organized Collapse: an Introduction to Discrete Morse Theory (Graduate Studies in Mathematics) (Graduate Studies in Mathematics, 207)
Publisher: American Mathematical Society
Publication Date: 2021
Language: English
ISBN 10: 1470464551
ISBN 13: 9781470464554
Binding: Soft cover
Condition: New

About this title

Synopsis

Applied topology is a modern subject which emerged in recent years at a crossroads of many methods, all of them topological in nature, which were used in a wide variety of applications in classical mathematics and beyond. Within applied topology, discrete Morse theory came into light as one of the main tools to understand cell complexes arising in different contexts, as well as to reduce the complexity of homology calculations. The present book provides a gentle introduction into this beautiful theory. Using a combinatorial approach―the author emphasizes acyclic matchings as the central object of study. The first two parts of the book can be used as a stand-alone introduction to homology, the last two parts delve into the core of discrete Morse theory. The presentation is broad, ranging from abstract topics, such as formulation of the entire theory using poset maps with small fibers, to heavily computational aspects, providing, for example, a specific algorithm of finding an explicit homology basis starting from an acyclic matching. The book will be appreciated by graduate students in applied topology, students and specialists in computer science and engineering, as well as research mathematicians interested in learning about the subject and applying it in context of their fields.

About the Author

Dmitry N. Kozlov: University of Bremen, Bremen, Germany and Okinawa Institute of Science and Technology, Okinawa, Japan

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