XXIst Oporto Meeting on Geometry, Topology and Physics, Lisbon Feb 7, 2015
http://cmup.fc.up.pt/cmup/omgtp/2015/home.html
On the topos foundation of persistence
GIT/TopoidalTDA/research/T5_etale
Abstract. Persistent homology has been extended in many different directions, permuting the encoding of topological features by barcodes and correspondent persistence diagrams.The set of points of all such diagrams determines a complete Heyting algebra that can explain aspects of the relations between correspondent persistence bars and provide a global perspective over this approach. Moreover, the topos of sheaves over the Heyting algebra of lifetimes determines a theory of sets with encoded lifetimes that provides us with an internal logic for persistence. In this talk we will discuss structural aspects of this algebra of lifetimes. We will also consider some concrete examples and compute their homology under this unified framework using the \'{e}tal\'{e} space construction.