2005/04/21 by Dmitry N. Kozlov · 1 citation
Computer Science · Mathematics · #cs.DM #math.RA
published as Comptes Rendus Mathematique, Acad. Sci. Paris, Ser. I 340 (2005), pp. 867-872
arxiv created 2005/04/21 · arxiv updated 2009/12/01
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⊕ T_*, where C_*^\cm is the Morse complex generated by the critical elements, and T_* is an acyclic complex.