9 citations · 55 across the 24 of their papers we have counts for
24 papers
Asymptotics of complex - symbols
Yunpeng Meng, Tian Yang
We study the - symbols -- an analytic extension of the -symbols for the principal series of the modular double of -- with complex…
Neutral representations of finite diagonalizable group schemes and fields of moduli
Giulio Bresciani, Angelo Vistoli, Tianzhi Yang
We introduce the notion of a neutral representation of a finite group, or finite group scheme, ; a representation with the property that if a gerbe over a fiel…
Asymptotics of quantum -symbols and generalized hyperbolic tetrahedra
Giulio Belletti, Tian Yang
We establish the geometry behind the quantum -symbols under only the admissibility conditions as in the definition of the Turaev-Viro invariants of -manifolds. As a classifi…
Asymptotics of quantum invariants of surface diffeomorphisms II: The figure-eight knot complement
Francis Bonahon, Helen Wong, Tian Yang
In earlier work, the authors introduced a conjecture which, for an orientation-preserving diffeomorphism of a surface, connects a certain quantum invariant of …
Asymptotics of quantum invariants of surface diffeomorphisms I: conjecture and algebraic computations
Francis Bonahon, Helen Wong, Tian Yang
The Kashaev-Murakami-Murakami Volume Conjecture connects the hyperbolic volume of a knot complement to the asymptotics of certain evaluations of the colored Jones polynomials of th…
Computation of leading coefficients in asymptotics of relative quantum invariants
Ka Ho Wong, Tian Yang
We propose Asymptotic Expansion Conjectures of the relative Reshetikhin-Turaev invariants, of the relative Turaev-Viro invariants and of the discrete Fourier transforms of the quan…
Adjoint twisted Reidemeister torsion and Gram matrices
Ka Ho Wong, Tian Yang
We compute the adjoint twisted Reidemeister torsion for closed oriented hyperbolic -manifolds and for hyperbolic -manifolds with toroidal boundary. In our formula, we conside…
Relative Reshetikhin-Turaev invariants, hyperbolic cone metrics and discrete Fourier transforms II
Ka Ho Wong, Tian Yang
We prove the Volume Conjecture for the relative Reshetikhin-Turaev invariants proposed in [29] for all pairs (M,K) such that M\K is homeomorphic to the complement of the figure-8 k…
A relative version of the Turaev-Viro invariants and the volume of hyperbolic polyhedral 3-manifolds
Tian Yang
We define a relative version of the Turaev-Viro invariants for an ideally triangulated compact 3-manifold with non-empty boundary and a coloring on the edges, generalizing the Tura…
Discrete Fourier transforms, quantum -symbols and deeply truncated tetrahedra
Giulio Belletti, Tian Yang
The asymptotic behavior of quantum -symbols is closely related to the volume of truncated hyperideal tetrahedra\,\cite{C}, and plays a central role in understanding the asympto…
Relative Reshetikhin-Turaev invariants, hyperbolic cone metrics and discrete Fourier transforms I
Ka Ho Wong, Tian Yang
We propose the Volume Conjecture for the relative Reshetikhin-Turaev invariants of a closed oriented -manifold with a colored framed link inside it whose asymptotic behavior is…
On the Volume Conjecture for hyperbolic Dehn-filled -manifolds along the figure-eight knot
Ka Ho Wong, Tian Yang
Using Ohtsuki's method, we prove the Asymptotic Expansion Conjecture and the Volume Conjecture of the Reshetikhin-Turaev and the Turev-Viro invariants for all hyperbolic -manifo…
On type-preserving representations of the thrice punctured projective plane group
Sara Maloni, Frédéric Palesi, Tian Yang
In this paper we consider type-preserving representations of the fundamental group of the three--holed projective plane into $\mathrm{PGL}(2, \R) =\mathrm{Isom}(\HH^2)$ and study t…
Growth of quantum 6j-symbols and applications to the Volume Conjecture
Giulio Belletti, Renaud Detcherry, Efstratia Kalfagianni +1
We prove the Turaev-Viro invariants volume conjecture for a "universal" class of cusped hyperbolic 3-manifolds that produces all 3-manifolds with empty or toroidal boundary by Dehn…
Turaev-Viro invariants, colored Jones polynomials and volume
Renaud Detcherry, Efstratia Kalfagianni, Tian Yang
We obtain a formula for the Turaev-Viro invariants of a link complement in terms of values of the colored Jones polynomial of the link. As an application we give the first examples…
Volume conjectures for the Reshetikhin-Turaev and the Turaev-Viro invariants
Qingtao Chen, Tian Yang
We consider the asymptotics of the Turaev-Viro and the Reshetikhin-Turaev invariants of a hyperbolic -manifold, evaluated at the root of unity instead…
On type-preserving representations of the four-punctured sphere group
Tian Yang
We give counterexamples to a question of Bowditch that if a non-elementary type-preserving representation of a punctured surface group…
Angle structures and hyperbolic -manifolds with totally geodesic boundary
Faze Zhang, Ruifeng Qiu, Tian Yang
This notes explores angle structures on ideally triangulated compact -manifolds with high genus boundary. We show that the existence of angle structures implies the existence of…
Volume and rigidity of hyperbolic polyhedral -manifolds
Feng Luo, Tian Yang
We investigate the rigidity of hyperbolic cone metrics on -manifolds which are isometric gluing of ideal and hyper-ideal tetrahedra in hyperbolic spaces. These metrics will be c…
The skein algebra of arcs and links and the decorated Teichmüller space
Julien Roger, Tian Yang
We define an associative algebra AS_h(S) generated by framed arcs and links over a punctured surface S which is a quantization of the Poisson algebra C(S) of arcs and curves on S.…
A deformation of Penner's simplicial coordinate
Tian Yang
We produce a one-parameter family of coordinates of the decorated Teichmüller space of an ideally triangulated punctured surface with negative Eu…
On the Hyperbolic Gluing Equations and Representations of Fundamental Groups of Closed 3-Manifolds
Tian Yang
We show that for a representation of the fundamental group of a triangulated closed 3-manifold (not necessarily hyperbolic) into $\PSL$ so that any edge loop has non-trivial image…
Thurston's Spinning Construction and Solutions to the Hyperbolic Gluing Equations for Closed Hyperbolic 3-Manifolds
Feng Luo, Stephan Tillmann, Tian Yang
We show that the hyperbolic structure on a closed, orientable, hyperbolic 3-manifold can be constructed from a solution to the hyperbolic gluing equations using any triangulation w…
A Batalin-Vilkovisky Algebra structure on the Hochschild Cohomology of Truncated Polynomials
Tian Yang
The main result of this paper is to calculate the Batalin-Vilkovisky structure of for and , a…