Titlebook: Research in Computational Topology 2; Ellen Gasparovic,Vanessa Robins,Katharine Turner Book 2022 The Editor(s) (if applicable) and The Aut

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Combinatorial Conditions for Directed Collapsing, of directed paths—are not always preserved. In this paper, we give computationally simple conditions for preserving the topology of past links. Furthermore, we give conditions for when link-preserving directed collapses preserve the contractability and connectedness of spaces of directed paths. Throughout, we provide illustrative examples.

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Ana Lucia Garcia-Pulido,Kathryn Hess,Jane Tan,Katharine Turner,Bei Wang,Naya Yerolemouust be described and quantified. Therefore, the chronological succession of events, their interpretation, management, and conflict resolution vary in accordance with a series of factors: local traditions, maritime culture, management instruments, institutions that manage the phenomenon, and the cust

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