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

Batan, Mehmet Ali

Pamuk, Mehmetcik

Varli, Hanife

English

arXiv

In this paper, we study the basic properties of persistent homotopy groups.
We show that the persistent fundamental group benefits from the Van Kampen
theorem, and the interleaving distance between total spaces is less than or
equal to the maximum of the interleaving distances between subspaces. We also
prove excision and Hurewicz theorems for persistent homotopy groups. As an
application, we analyze the sublevelset persistent homotopy groups of the
energy landscape of alkane molecules.Comment: 29 pages, 20 figure

Persistent Homotopy

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