License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SoCG.2018.54
URN: urn:nbn:de:0030-drops-87671
URL: https://drops.dagstuhl.de/opus/volltexte/2018/8767/
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Knudson, Kevin ; Wang, Bei

Discrete Stratified Morse Theory: A User's Guide

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LIPIcs-SoCG-2018-54.pdf (0.7 MB)

Abstract

Inspired by the works of Forman on discrete Morse theory, which is a combinatorial adaptation to cell complexes of classical Morse theory on manifolds, we introduce a discrete analogue of the stratified Morse theory of Goresky and MacPherson. We describe the basics of this theory and prove fundamental theorems relating the topology of a general simplicial complex with the critical simplices of a discrete stratified Morse function on the complex. We also provide an algorithm that constructs a discrete stratified Morse function out of an arbitrary function defined on a finite simplicial complex; this is different from simply constructing a discrete Morse function on such a complex. We borrow Forman's idea of a "user's guide," where we give simple examples to convey the utility of our theory.

BibTeX - Entry

@InProceedings{knudson_et_al:LIPIcs:2018:8767,
  author =	{Kevin Knudson and Bei Wang},
  title =	{{Discrete Stratified Morse Theory: A User's Guide}},
  booktitle =	{34th International Symposium on Computational Geometry (SoCG 2018)},
  pages =	{54:1--54:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-066-8},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{99},
  editor =	{Bettina Speckmann and Csaba D. T{\'o}th},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/8767},
  URN =		{urn:nbn:de:0030-drops-87671},
  doi =		{10.4230/LIPIcs.SoCG.2018.54},
  annote =	{Keywords: Discrete Morse theory, stratified Morse theory, topological data analysis}
}

Keywords: Discrete Morse theory, stratified Morse theory, topological data analysis
Collection: 34th International Symposium on Computational Geometry (SoCG 2018)
Issue Date: 2018
Date of publication: 08.06.2018

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