Article Per Year (5 Year)
p-Index From 2021 - 2026
0
P-Index
This Author published in this journals
All Journal Journal of the Indonesian Mathematical Society
Yasuaki Hiraoka
Institute of Mathematics for Industry, Kyushu University
Mathematics

Published : 1 Documents Claim Missing Document
Claim Missing Document
Check
Articles

Found 1 Documents
Search

 1 
MORSE REDUCTION FOR ZIGZAG COMPLEXES Emerson Escolar; Yasuaki Hiraoka
Journal of the Indonesian Mathematical Society Volume 20 Number 1 (April 2014)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.20.1.177.47-75

Abstract

A paper by Mischaikow and Nanda [14] uses filtered acyclic matchingsto form a Morse filtration for a filtered complex. The Morse filtration is smallerin size, yet has persistent homology equivalent to that of the original. We give anextension of acyclic matchings to the case of zigzag complexes and prove that theMorse zigzag complex similarly obtained has zigzag homology isomorphic to thatof the original. We present an algorithm to compute a Morse zigzag complex for agiven zigzag complex and some numerical examples. Since the Morse zigzag complexis smaller in size, calculations of its zigzag homology tend to complete faster thanthose for the original zigzag complex.DOI : http://dx.doi.org/10.22342/jims.20.1.177.47-75
Co-Authors Emerson Escolar