5 papers
Power sum elements in the skein algebra
Bodie Beaumont-Gould, Erik Brodsky, Vijay Higgins +3
We study the skein algebras of surfaces associated to the exceptional Lie group using Kuperberg webs. We identify two 2-variable polynomials, and and…
Constructions of -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…
Turaev-Viro invariants and cabling operations
Sanjay Kumar, Joseph M. Melby
In this paper, we study the variation of the Turaev--Viro invariants for -manifolds with toroidal boundary under the operation of attaching a -cable space. We apply our r…
Asymptotic additivity of the Turaev-Viro invariants for a family of -manifolds
Sanjay Kumar, Joseph M. Melby
In this paper, we show that the Turaev-Viro invariant volume conjecture posed by Chen and Yang is preserved under gluings of toroidal boundary components for a family of -manifo…
Guts and volume for hyperbolic -orbifolds with underlying space
Christopher K. Atkinson, Jessica Mallepalle, Joseph Melby +2
For a hyperbolic -orbifold with underlying space the -sphere, we obtain a lower bound on its volume in the case that it contains an essential -suborbifold with underlying…