Akademik Veri Yönetim Sistemi
Tezin Türü: Yüksek Lisans
Tezin Yürütüldüğü Kurum: Orta Doğu Teknik Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, Türkiye
Tezin Onay Tarihi: 2019
Öğrenci: Mehmet Ali Batan
Danışman: MEHMETCİK PAMUK
Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
Özet: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.