6 citations · 20 across the 8 of their papers we have counts for
10 papers
Symmetry groups of flat fully augmented links and their complements
Christian Millichap, Rolland Trapp
In this paper, we prove that the (orientation-preserving) symmetry groups of -prime flat fully augmented links correspond exactly with the finite subgroups of . We accompl…
Symmetry groups of hyperbolic links and their complements
Christian Millichap, Rolland Trapp
We explicitly construct a sequence of hyperbolic links where the number of symmetries of each that are not induced by symmetries of…
Flat fully augmented links are determined by their complements
Christian Millichap, Rolland Trapp
In this paper, we show that two flat fully augmented links with homeomorphic complements must be equivalent as links in . This requires a careful analysis of how to…
Dehn surgery and hyperbolic knot complements without hidden symmetries
Eric Chesebro, Jason DeBlois, Neil R Hoffman +3
Neumann and Reid conjecture that there are exactly three knot complements which admit hidden symmetries. This paper establishes several results that provide evidence for the conjec…
Symmetries and hidden symmetries of -twisted knot complements
Neil R. Hoffman, Christian Millichap, William Worden
In this paper we analyze symmetries, hidden symmetries, and commensurability classes of -twisted knot complements, which are the complements of knots that have a sufficie…
Arithmeticity and Hidden Symmetries of Fully Augmented Pretzel Link Complements
Jeffrey S. Meyer, Christian Millichap, Rolland Trapp
This paper examines number theoretic and topological properties of fully augmented pretzel link complements. In particular, we determine exactly when these link complements are ari…
Spectrally similar incommensurable 3-manifolds
David Futer, Christian Millichap
Reid has asked whether hyperbolic manifolds with the same geodesic length spectrum must be commensurable. Building toward a negative answer to this question, we construct examples…
Hidden Symmetries and Commensurability of 2-Bridge Link Complements
Christian Millichap, William Worden
In this paper, we show that any non-arithmetic hyperbolic -bridge link complement admits no hidden symmetries. As a corollary, we conclude that a hyperbolic -bridge link comp…
Mutations and short geodesics in hyperbolic 3-manifolds
Christian Millichap
In this paper, we explicitly construct large classes of incommensurable hyperbolic knot complements with the same volume and the same initial (complex) length spectrum. Furthermore…
Factorial growth rates for the number of hyperbolic 3-manifolds of a given volume
Christian Millichap
The work of Jørgensen and Thurston shows that there is a finite number N(v) of orientable hyperbolic 3-manifolds with any given volume v. In this paper, we construct examples showi…