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arXiv · 1708.02055

Directed path spaces via discrete vector fields

Krzysztof Ziemiański
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Abstract

Let $K$ be an arbitrary semi-cubical set that can be embedded in a standard cube. Using Discrete Morse Theory, we construct a CW-complex that is homotopy equivalent to the space $\vec{P}(K)_v^w$ of directed paths between two given vertices $v,w$ of $K$. In many cases, this construction is minimal: the cells of the constructed CW-complex are in 1--1 correspondence with the generators of the homology of $\vec{P}(K)_v^w$.

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Krzysztof Ziemiański. 2017-08-07. Directed path spaces via discrete vector fields. https://arxiv.org/abs/1708.02055

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