Persistent Homotopy

In this paper, we study some of the basic properties of persistent homotopy. We show that persistent fundamental group benefits from the Van Kampen theorem and the interleaving distance between total spaces is the maximum of the interleaving distances between subspaces. Moreover, we prove excision and Hurewicz theorems for persistent homotopy groups.Comment: 16 pages, 13 figure

Kararlı temek grubu için Van Kampen teoremi.

Persistent homotopy is one of the newest algebraic topology methods in order to understand and capture topological features of discrete objects or point data clouds (the set of points with metric defined on it). On the other hand, in algebraic topology, the Van Kampen Theorem is a great tool to determine fundamental group of complicated spaces in terms of simpler subspaces whose fundamental groups are already known. In this thesis, we show that Van Kampen Theorem is still valid for the persistent fundamental group. Finally, we show that interleavings, a way to compare persistences, among subspaces imply interleavings among total spaces.Thesis (M.S.) -- Graduate School of Applied Mathematics. Mathematics