Dowker’s Theorem by Simplicial Sets and a Category of 0-Interleavings

Abstract

In this thesis we look at an alternative proof of Dowker’s theorem [4] using simplical sets. We prove the strongest version of the theorem [3], which can be applied to persistence homology in the sense that every nested sequence of relations gives two filtered simplicial complexes with the same persistence homology. We also compare the category of filtered simplicial complexes with the category of dissimilarities, and see how this leads to a nice category of 0-interleaved filtered simplicial complexes.