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Morse Chain Complex from Forman Gradient in 3D with \(\mathbb {Z}_2\) Coefficients

  • Lidija ČomićEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9667)

Abstract

A Forman gradient V on a cell complex \(\varGamma \) enables efficient computation of the homology of \(\varGamma \): the Morse chain complex defined by critical cells of V and their connection through gradient V-paths is equivalent to the homology of chain complex defined by cells of \(\varGamma \) and the immediate boundary relation between them.

We propose an algorithm that computes the boundary operator of the Morse chain complex associated with Forman gradient V defined on a regular cell 3-complex \(\varGamma \). The algorithm computes the boundary operator with coefficients in \(\mathbb {Z}_2\), and encodes it in the form of the boundary matrix. Our algorithm is incremental: as it progresses through a filtration of \(\varGamma \) induced by V, it computes the boundary operator for each critical cell reached in the filtration order.

Keywords

Morse chain complex Forman gradient 

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Faculty of Technical SciencesUniversity of Novi SadNovi SadSerbia

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