Title: Data and homotopy types
Speaker: Rick Jardine
Speaker Info: Western University
Homotopy theoretic approaches to the study of the Vietoris-Rips complex V(X) will be summarized. The category of inductive objects in simplicial sets is a context for the discussion of interleavings.Date: Monday, May 13, 2019
If X is included in a data set Y and if X is sufficiently dense in Y (suitably defined), then there is an explicit space-level interleaving construction relating the respective Vietoris-Rips filtrations. This construction leads to a stability result: the objects V(X) and V(Y) are weakly equivalent in sections for sufficiently large distance parameters, where the range of those parameters is determined by the level of density of X in Y. The same construction also applies to give a stability result for the Lesnick subobjects of the Vietoris-Rips system.