Please use this identifier to cite or link to this item: https://hdl.handle.net/10356/156888
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
Fulltext Permission: restricted
Fulltext Availability: With Fulltext
Appears in Collections:SPMS Student Reports (FYP/IA/PA/PI)

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