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Infinitely Many Knots With NonIntegral Trace

https://doi.org/10.1080/10586458.2021.1980461

Reid, A. W. ; Rouse, N. ( October 2021 , Experimental Mathematics)

We prove that there are infinitely many non-homeomorphic hyperbolic knot complements S³∖Kᵢ=H³/Γᵢ for which Γᵢ contains elements whose trace is an algebraic non-integer.
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Sequences of high rank lattices with large systole containing a fixed genus surface group

Long, D.D ; Reid, A. W. ( January 2019 , New York journal of mathematics)

In this paper we exhibit sequences of torsion-free lattices (both uniform and non-uniform) that have arbitrarily large systole, but all containing a thin surface subgroup of fixed genus.
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Determining hyperbolic 3-manifolds by their surfaces

https://doi.org/10.1090/proc/14219

McReynolds, D. B. ; Reid, A. W. ( January 2019 , Proceedings of the American Mathematical Society)

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