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Title: | On the L2-torsion of the figure-of-eight knot complement | Authors: | Teo, Joven Jia Xuan | Keywords: | Science::Mathematics::Topology | Issue Date: | 2022 | Publisher: | Nanyang Technological University | Source: | 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 | Abstract: | 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. | URI: | https://hdl.handle.net/10356/156888 | Schools: | School of Physical and Mathematical Sciences | Fulltext Permission: | restricted | Fulltext Availability: | With Fulltext |
Appears in Collections: | SPMS Student Reports (FYP/IA/PA/PI) |
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