Discrete Morse Theory

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Kashkouie, Fatemeh | 2015

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 48693 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Fanai, Hamid Reza
Abstract:
A number of questions from a variety of areas of mathematics lead one to the problem of analyzing the topology of a simplicial complex. However, there are few general techniques available to aid us in this study. On the other hand, some very general theories have been developed for the study of smooth manifolds. One of the most powerful, and useful, of these theories is Morse Theory. We present a combinatorial adaptation of Morse Theory, which we call discrete Morse theory that may be applied to any simplicial complex (or more general cell complex). Our goal is to present an overview of the subject of discrete Morse Theory that is sufficient both to understand the major applications of the theory to combinatorics, and to apply the theory to new problems
Keywords:
Simplicial Complex ; Combinations ; Discrete Morse Theory ; Cell Complex ; Smooth Manifolds