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Van Kampen theorem for persistent fundamental group

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2019
Batan, Mehmet Ali
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.