Geometry of biperiodic alternating links
| Autor: | Jessica S. Purcell, Abhijit Champanerkar, Ilya Kofman |
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| Rok vydání: | 2018 |
| Předmět: |
Pure mathematics
57M27 57M50 57M25 010308 nuclear & particles physics General Mathematics 010102 general mathematics Triangulation (social science) Geometric Topology (math.GT) Torus 01 natural sciences Mathematics - Geometric Topology Unimodular matrix Hyperbolic set 0103 physical sciences Euclidean geometry FOS: Mathematics 0101 mathematics Invariant (mathematics) Link (knot theory) Quotient Mathematics |
| Zdroj: | Journal of the London Mathematical Society. 99:807-830 |
| ISSN: | 1469-7750 0024-6107 |
| DOI: | 10.1112/jlms.12195 |
| Popis: | A biperiodic alternating link has an alternating quotient link in the thickened torus. In this paper, we focus on semi-regular links, a class of biperiodic alternating links whose hyperbolic structure can be immediately determined from a corresponding Euclidean tiling. Consequently, we determine the exact volumes of semi-regular links. We relate their commensurability and arithmeticity to the corresponding tiling, and assuming a conjecture of Milnor, we show there exist infinitely many pairwise incommensurable semi-regular links with the same invariant trace field. We show that only two semi-regular links have totally geodesic checkerboard surfaces; these two links satisfy the Volume Density Conjecture. Finally, we give conditions implying that many additional biperiodic alternating links are hyperbolic and admit a positively oriented, unimodular geometric triangulation. We also provide sharp upper and lower volume bounds for these links. 25 pages, 15 figures. V2: Minor changes. Added reference, fixed typos, and clarified proof of Theorem 5.1 |
| Databáze: | OpenAIRE |
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