The Dowker theorem via discrete Morse theory
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914880776306688 |
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| author | Brun, Morten Grinberg, Darij |
| author_facet | Brun, Morten Grinberg, Darij |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_15454 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Dowker theorem via discrete Morse theory Brun, Morten Grinberg, Darij Combinatorics Algebraic Topology 57Q10, 55-01, 55U10 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. |
| title | The Dowker theorem via discrete Morse theory |
| topic | Combinatorics Algebraic Topology 57Q10, 55-01, 55U10 |
| url | https://arxiv.org/abs/2407.15454 |