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Preprint
The Dowker theorem via discrete Morse theory
ArXiv.org
22 Jul 2024
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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Details
- Title
- The Dowker theorem via discrete Morse theory
- Creators
- Morten BrunDarij Grinberg
- Publication Details
- ArXiv.org
- Resource Type
- Preprint
- Language
- English
- Academic Unit
- Mathematics
- Other Identifier
- 991021894606004721