Flattening knotted surfaces
| Autor: | Horvat, Eva |
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| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Geometriae Dedicata, volume 217, Article number: 36 (2023) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s10711-023-00770-6 |
| Popis: | A knotted surface in the 4-sphere may be described by means of a hyperbolic diagram that captures the 0-section of a special Morse function, called a hyperbolic decomposition. We show that every hyperbolic decomposition of a knotted surface K defines a projection of K onto a 2-sphere, whose set of critical values is the hyperbolic diagram of K. We apply such projections, called flattenings, to define three invariants of knotted surfaces: the layering, the trunk and the partition number. The basic properties of flattenings and their derived invariants are obtained. Our construction is used to study flattenings of satellite 2-knots. Comment: 25 pages, 16 figures |
| Databáze: | arXiv |
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