Volumes, Lorenz-like templates, and braids
| Autor: | de Paiva, Thiago, Hui, Connie On Yu, Migueles, José Andrés Rodríguez |
|---|---|
| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Lorenz-like templates are obtained from applying half twists to the two strips of the Lorenz template. Ghrist proved that infinitely many of these templates are universal, meaning they contain all links in the 3-sphere. In this paper, we generalise the bunch algorithm to construct links embedded in universal Lorenz-like templates and provide an upper volume bound that is quadratic in the trip number. We also establish a correspondence between links embedded in these universal Lorenz-like templates and generalised T-links. While generalised T-links have appeared in the knot theory literature before, we prove that they are, in fact, all links in the 3-sphere. Thus, we can regard each link in the 3-sphere as a generalised T-link, which has an associated Lorenz link. We use the upper bound obtained from the generalised bunch algorithm to provide an upper volume bound for all hyperbolic link complements in the 3-sphere. Such a bound grows quadratically in terms of the braid indexes of the associated Lorenz links. Comment: 24 pages, 6 figures |
| Databáze: | arXiv |
| Externí odkaz: |
|