Joseph M. Melby

collaborators

3 papers

math.GT2023

Power sum elements in the $G_{2}$ skein algebra

Bodie Beaumont-Gould, Erik Brodsky, Vijay Higgins +3

We study the skein algebras of surfaces associated to the exceptional Lie group $G_{2},$ using Kuperberg webs. We identify two 2-variable polynomials, $P_{n} (x, y)$ and $Q_{n} (x, y),$ and…

math.GT2023

Constructions of $q$ -hyperbolic knots

Efstratia Kalfagianni, Joseph M. Melby

We use Dehn surgery methods to construct infinite families of hyperbolic knots in the 3-sphere satisfying a weak form of the Turaev--Viro invariants volume conjecture. The results…

math.GT2017

Guts and volume for hyperbolic $3$ -orbifolds with underlying space $S^{3}$

Christopher K. Atkinson, Jessica Mallepalle, Joseph Melby +2

For a hyperbolic $3$ -orbifold with underlying space the $3$ -sphere, we obtain a lower bound on its volume in the case that it contains an essential $2$ -suborbifold with underlying…

Power sum elements in the G2​ skein algebra

Constructions of q-hyperbolic knots

Guts and volume for hyperbolic 3-orbifolds with underlying space S3

Power sum elements in the $G_{2}$ skein algebra

Constructions of $q$ -hyperbolic knots

Guts and volume for hyperbolic $3$ -orbifolds with underlying space $S^{3}$