Discrete Morse Theory for free chain complexes

Details Discrete Morse Theory for free chain complexes Discrete Morse Theory for free chain complexes

2005-04-21

arxiv.org/abs/cs/0504090v1

Comptes Rendus Mathematique, Acad. Sci. Paris, Ser. I 340 (2005), pp. 867-872

Computer Science

Discrete Mathematics

Scientific paper

We extend the combinatorial Morse complex construction to the arbitrary free chain complexes, and give a short, self-contained, and elementary proof of the quasi-isomorphism between the original chain complex and its Morse complex. Even stronger, the main result states that, if $C_*$ is a free chain complex, and $\cm$ an acyclic matching, then $C_*=C_*^\cm\oplus T_*$, where $C_*^\cm$ is the Morse complex generated by the critical elements, and $T_*$ is an acyclic complex.

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