Homology under monotone maps between finite topological spaces

2013/12/04 by Patrick Erik Bradley, Bradley, Patrick Erik
Mathematics · #55N10 #Algebraic Topology (math.AT) #FOS: Mathematics #math.AT #msc:55N10

paper · pdf · doi:10.48550/arxiv.1312.1191

Main result Theorem 3.3 is incorrect

arxiv created 2018/01/10 · arxiv updated 2018/01/11

Abstract

It is shown that a surjective monotone map X→ Y between finite T₀-spaces induces a surjective map on homology. As such a map turns out to be a sequence of edge contractions in the Hasse diagram of X, followed by a homeomorphism, this leads to an explicit relation between the Betti numbers of X to those of Y and the cokernels of the edge contraction maps on the order complexes.

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