MORSE REDUCTION FOR ZIGZAG COMPLEXES

Emerson Escolar, Yasuaki Hiraoka

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


Keywords


Applied topology, Homology, Zigzag persistence, Acyclic matching

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DOI: https://doi.org/10.22342/jims.20.1.177.47-75

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Journal of the Indonesian Mathematical Society
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