Trisecting a 4-dimensional book into three chapters
We describe an algorithm that takes as input an open book decomposition of a closed oriented 4-manifold and outputs an explicit trisection diagram of that 4-manifold. Moreover, a slight variation of this algorithm also works for open books on manifolds with non-empty boundary and for 3-manifold bund...
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| Main Authors: | , |
|---|---|
| Format: | Article (Journal) |
| Language: | English |
| Published: |
25 June 2024
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| In: |
Geometriae dedicata
Year: 2024, Volume: 218, Issue: 4, Pages: 1-33 |
| ISSN: | 1572-9168 |
| DOI: | 10.1007/s10711-024-00932-0 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1007/s10711-024-00932-0 Verlag, lizenzpflichtig, Volltext: https://link.springer.com/article/10.1007/s10711-024-00932-0 
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| Author Notes: | Marc Kegel, Felix Schmäschke |
MARC
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| 520 | |a We describe an algorithm that takes as input an open book decomposition of a closed oriented 4-manifold and outputs an explicit trisection diagram of that 4-manifold. Moreover, a slight variation of this algorithm also works for open books on manifolds with non-empty boundary and for 3-manifold bundles over $$S^1$$. We apply this algorithm to several simple open books, demonstrate that it is compatible with various topological constructions, and argue that it generalizes and unifies several previously known constructions. | ||
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