Persistence in discrete Morse theory

Ulrich Bauer

doi:10.53846/goediss-2536

Persistence in discrete Morse theory

Ulrich Bauer

Associate Professorship of Applied Topology and Geometry

Research output: Types of Thesis › Doctoral Thesis

Abstract

The goal of this thesis is to bring together two different theories about critical points of a scalar function and their relation to topology: Discrete Morse theory and Persistent homology. While the goals and fundamental techniques are different, there are certain themes appearing in both theories that closely resemble each other. In certain cases, the two threads can be joined, leading to new insights beyond the classical realm of one particular theory.

Original language	American English
Qualification	Doctor of Philosophy
Awarding Institution	Georg-August Universität Göttingen
Supervisors/Advisors	Wardetzky, Max, Supervisor, External person
Date of Award	22 Jul 2011
DOIs	https://doi.org/10.53846/goediss-2536
State	Published - 15 Jul 2011

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abstract = "The goal of this thesis is to bring together two different theories about critical points of a scalar function and their relation to topology: Discrete Morse theory and Persistent homology. While the goals and fundamental techniques are different, there are certain themes appearing in both theories that closely resemble each other. In certain cases, the two threads can be joined, leading to new insights beyond the classical realm of one particular theory.",

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AB - The goal of this thesis is to bring together two different theories about critical points of a scalar function and their relation to topology: Discrete Morse theory and Persistent homology. While the goals and fundamental techniques are different, there are certain themes appearing in both theories that closely resemble each other. In certain cases, the two threads can be joined, leading to new insights beyond the classical realm of one particular theory.

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Persistence in discrete Morse theory

Abstract

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