MORSE REDUCTION FOR ZIGZAG COMPLEXES - Emerson Escolar; Yasuaki Hiraoka (IndoMS, 2014)
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