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arXiv · 2407.15454

The Dowker theorem via discrete Morse theory

Morten Brun·Darij Grinberg
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Abstract

The Dowker theorem is a classical result in the topology of finite spaces, claiming that any binary relation between two finite spaces defines two homotopy-equivalent complexes (the Dowker complexes). Recently, Barmak strengthened this to a simple-homotopy-equivalence. We reprove Barmak's result using a combinatorial argument that constructs an explicit acyclic matching in the sense of discrete Morse theory.

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Morten Brun, Darij Grinberg. 2024-07-22. The Dowker theorem via discrete Morse theory. https://arxiv.org/abs/2407.15454

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