$P$-persistent homology of finite topological spaces

Alice Patania; Francesco Vaccarino; Giovanni Petri

arxiv: 1502.04873 · v1 · pith:H3R43AQSnew · submitted 2015-02-17 · 🧮 math.AT · cs.CG· math.CO· math.CT

P-persistent homology of finite topological spaces

Francesco Vaccarino , Alice Patania , Giovanni Petri This is my paper

classification 🧮 math.AT cs.CGmath.COmath.CT

keywords finitepersistenthomologyspacestopologicalcategorycliquecomplex

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Let $P$ be a finite poset. We will show that for any reasonable $P$-persistent object $X$ in the category of finite topological spaces, there is a $P-$ weighted graph, whose clique complex has the same $P$-persistent homology as $X$.

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P-persistent homology of finite topological spaces

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