Construction of the discrete Morse complex in the non-compact case

Abstract

We prove an infinite analogue of the main theorem of discrete Morse theory formulated in terms of discrete Morse matchings. Our theorem holds under the assumption that the given Morse matching induces finitely many equivalence classes of infinite directed simple paths. A homological version of the theorem is also given.

arXiv comment12 pages; change of title, some new references and new Theorem 4.4