7 papers
A relation between the Baseilhac-Benedetti and the Bonahon-Liu-Wong-Yang invariants
Stavros Garoufalidis, Tao Yu
Baseilhac-Benedetti, following ideas of Kashaev, introduced invariants of pseudo-Anosov homeomorphisms of punctured hyperbolic surfaces that depend on a complex root of unity of od…
On the Bonahon--Wong--Yang invariants of pseudo-Anosov maps
Stavros Garoufalidis, Tao Yu
We conjecture (and prove for once-punctured torus bundles) that the Bonahon--Wong--Yang invariants of pseudo-Anosov homeomorphisms of a punctured surface at roots of unity coincide…
The 3d-index of the 3d-skein module via the quantum trace map
Stavros Garoufalidis, Tao Yu
We define a map from the skein module of a cusped hyperbolic 3-manifold to the ring of Laurent series in one variable with integer coefficients that satisfies two properties: its e…
A Quantum trace map for 3-manifolds
Stavros Garoufalidis, Tao Yu
We define a quantum trace map from the skein module of a 3-manifold with torus boundary components to a module (left and right quotient of a quantum torus) constructed from an idea…
Explicit representations and Azumaya loci of skein algebras of small surfaces
Tao Yu
We construct finite dimensional representations of the Kauffman bracket skein algebra of the one-punctured torus and four-punctured sphere at all roots of unity. The representation…
Center of the stated skein algebra
Tao Yu
The stated skein algebra is a generalization of the Kauffman bracket skein algebra introduced in the study of quantum trace maps. When the quantum parameter is a root of unity, the…
Left-invariant Ricci collineations associated to Yano connections on three-dimensional Lorentzian Lie groups
Tao Yu
In this paper, we classify Left-invariant Ricci collineations associated to Yano connections on three-dimensional Lorentzian Lie groups.