On the L2-torsion of the figure-of-eight knot complement
For each prime p congruent to 1 modulo 6, we construct a cover of the figure-of-eight knot complement and describe its structure as a Z-CW-complex. We then state a conjecture relating the limit of the L2-torsion of these covers as p approaches infinity to the L2-torsion of the universal cover, which...
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| Format: | Final Year Project |
| Language: | English |
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Nanyang Technological University
2022
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| Online Access: | https://hdl.handle.net/10356/156888 |
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| Institution: | Nanyang Technological University |
| Language: | English |
| Summary: | For each prime p congruent to 1 modulo 6, we construct a cover of the figure-of-eight knot complement and describe its structure as a Z-CW-complex. We then state a conjecture relating the limit of the L2-torsion of these covers as p approaches infinity to the L2-torsion of the universal cover, which is known to be proportional to the hyperbolic volume of the figure-of-eight knot complement. Both numerical evidence and theoretical results in this direction are then presented. In particular, we prove that the L2-torsion in this case can be expressed as the Mahler measure of the characteristic polynomial of a certain block matrix built up from permutation matrices. |
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