Universality of the Homotopy Interleaving Distance

Tuesday, March 25, 2014 - 1:30pm - 2:30pm
Lind 305
Michael Lesnick (University of Minnesota, Twin Cities)
We observe that two key results about the persistence barcodes of point cloud data can be lifted to statements about filtrations, formulated directly on the topological level, given a choice of pseudometric on filtrations satisfying (i) a stability property and (ii) a homotopy invariance property. We introduce a pseudometric d_{HI}, the homotopy interleaving distance, satisfying these properties. We show that d_{HI} is universal in a sense analogous to which the bottleneck distance on persistence barcodes is universal: Namely, we show that if d is another distance on filtrations satisfying properties (i) and (ii) then d leq d_{HI}.

This is joint work with Andrew Blumberg.