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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Nanyang Technological University
2022
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sg-ntu-dr.10356-1568882023-02-28T23:18:41Z On the L2-torsion of the figure-of-eight knot complement Teo, Joven Jia Xuan Andrew James Kricker School of Physical and Mathematical Sciences AJKricker@ntu.edu.sg Science::Mathematics::Topology 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. Bachelor of Science in Mathematical Sciences 2022-04-27T05:54:06Z 2022-04-27T05:54:06Z 2022 Final Year Project (FYP) Teo, J. J. X. (2022). On the L2-torsion of the figure-of-eight knot complement. Final Year Project (FYP), Nanyang Technological University, Singapore. https://hdl.handle.net/10356/156888 https://hdl.handle.net/10356/156888 en application/pdf Nanyang Technological University |
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Singapore Singapore |
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Science::Mathematics::Topology |
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Science::Mathematics::Topology Teo, Joven Jia Xuan On the L2-torsion of the figure-of-eight knot complement |
| description |
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. |
| author2 |
Andrew James Kricker |
| author_facet |
Andrew James Kricker Teo, Joven Jia Xuan |
| format |
Final Year Project |
| author |
Teo, Joven Jia Xuan |
| author_sort |
Teo, Joven Jia Xuan |
| title |
On the L2-torsion of the figure-of-eight knot complement |
| title_short |
On the L2-torsion of the figure-of-eight knot complement |
| title_full |
On the L2-torsion of the figure-of-eight knot complement |
| title_fullStr |
On the L2-torsion of the figure-of-eight knot complement |
| title_full_unstemmed |
On the L2-torsion of the figure-of-eight knot complement |
| title_sort |
on the l2-torsion of the figure-of-eight knot complement |
| publisher |
Nanyang Technological University |
| publishDate |
2022 |
| url |
https://hdl.handle.net/10356/156888 |
| _version_ |
1759857821324673024 |