Fetching the paper…
Reading the bibliography…
In their recent work, Garoufalidis and Kashaev extended the 3D-index of an ideally triangulated 3-manifold with toroidal boundary to a well-defined topological invariant which takes the form of a meromorphic function of 2 complex variables per boundary component and which depends in addition on a quantisation parameter q.
A transformation of the generalised hypergeometric series
Ernest W. Barnes · 1910
Earlier work this paper cites.
On the Lerch zeta function
Tom M. Apostol · 1951
Earlier work this paper cites.
Higher transcendental functions
Arthur Erdélyi et al · 1953
Earlier work this paper cites.
Generalized hypergeometric functions
Lucy Joan Slater · 1966
Earlier work this paper cites.
Volumes of hyperbolic three-manifolds
Walter Neumann and Don Zagier · 1985
Earlier work this paper cites.
On ideal points of deformation curves of hyperbolic 3-manifolds with one cusp
Tomoyoshi Yoshida · 1991
Earlier work this paper cites.
Combinatorics of triangulations and the Chern–Simons invariant for hyperbolic 3 3 -manifolds
Walter Neumann · 1992
Earlier work this paper cites.
Mellin transforms and asymptotics: harmonic sums
Philippe Flajolet, Xavier Gourdon, and Philippe Dumas · 1995
Earlier work this paper cites.
A link invariant from quantum dilogarithm
Rinat M. Kashaev · 1995
Earlier work this paper cites.
Dilogarithm identities
Anatol N. Kirillov · 1995
Earlier work this paper cites.
The hyperbolic volume of knots from the quantum dilogarithm
Rinat M. Kashaev · 1997
Earlier work this paper cites.
Torsion de Reidemeister pour les variétés hyperboliques
Joan Porti · 1997
Earlier work this paper cites.
Normal surface Q-theory
Jeffrey L. Tollefson · 1998
Earlier work this paper cites.
Some asymptotic formulae for q q -shifted factorials
Richard J. McIntosh · 1999
Earlier work this paper cites.
The colored Jones polynomials and the simplicial volume of a knot
Hitoshi Murakami and Jun Murakami · 2001
Earlier work this paper cites.
Asymptotics and Mellin–Barnes Integrals
Richard B. Paris and David Kaminski · 2001
Earlier work this paper cites.
The geometry and topology of three-manifolds
William Thurston · 2002
Earlier work this paper cites.
Positively oriented ideal triangulations on hyperbolic three-manifolds
Young-Eun Choi · 2004
Cited alongside, same era.
Hyperbolic volume of representations of fundamental groups of cusped 3-manifolds
Stefano Francaviglia · 2004
Cited alongside, same era.
The variety of characters in P S L ( 2 , ℂ ) PSL(2,\mathbb{C})
Michael Heusener and Joan Porti · 2004
Cited alongside, same era.
The dilogarithm function
Don Zagier · 2007
Cited alongside, same era.
The volume and Chern–Simons invariant of a representation
Christian K. Zickert · 2009
Cited alongside, same era.
From angled triangulations to hyperbolic structures
David Futer and François Guéritaud · 2011
Cited alongside, same era.
1-eficient triangulations and the index of a cusped hyperbolic 3-manifold
Stavros Garoufalidis, Craig D. Hodgson, J. Hyam Rubinstein, and Henry Segerman · 2015
Later among the works it cites.
The complex volume of S L ( n , ℂ ) SL(n,\mathbb{C}) -representations of 3 3 -manifolds
Stavros Garoufalidis, Dylan P. Thurston and Christian K. Zickert · 2015
Later among the works it cites.
On the asymptotic expansion of the q q -dilogarithm
Fethi Bouzeffour and Borhen Halouani · 2016
Later among the works it cites.
The 3D index of an ideal triangulation and angle structures
Stavros Garoufalidis · 2016
Later among the works it cites.
The 3D-index and normal surfaces
Stavros Garoufalidis, Craig D. Hodgson, Neil R. Hoffman and J. Hyam Rubinstein · 2016
Later among the works it cites.
A TQFT of Turaev–Viro type on shaped triangulations
Rinat M. Kashaev, Feng Luo, and Grigory Vartanov · 2016
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
A TQFT from quantum Teichmüller theory
Jørgen Ellegaard Andersen and Rinat Kashaev · 2012
Cited alongside, same era.
Triangulations of hyperbolic 3 3 -manifolds admitting strict angle structures
Craig D. Hodgson, J. Hyam Rubinstein, and Henry Segerman · 2012
Cited alongside, same era.
A new formulation of the Teichmüller TQFT
Jørgen Ellegaard Andersen and Rinat Kashaev · 2013
Cited alongside, same era.
Quantum Riemann surfaces in Chern-Simons theory
Tudor Dimofte · 2013
Cited alongside, same era.
3-manifolds and 3D indices
Tudor Dimofte, Davide Gaiotto, and Sergei Gukov · 2013
Cited alongside, same era.
The quantum content of the gluing equations
Tudor Dimofte and Stavros Garoufalidis · 2013
Cited alongside, same era.
Later among the works it cites.
Solving Thurston’s equation in a commutative ring
Feng Luo · 2016
Later among the works it cites.
On the geometric meaning of the non-abelian Reidemeister torsion of cusped hyperbolic 3-manifolds
Rafał Siejakowski · 2017
Later among the works it cites.
Volume conjectures for the Reshetikhin–Turaev and the Turaev–Viro invariants
Qingtao Chen and Tian Yang · 2018
Later among the works it cites.
A meromorphic extension of the 3D-index
Stavros Garoufalidis and Rinat Kashaev · 2019
Later among the works it cites.
Traversing three-manifold triangulations and spines
J. Hyam Rubinstein, Henry Segerman, Stephan Tillmann · 2019
Later among the works it cites.
Regina: Software for low-dimensional topology
B. Burton, R. Budney, W. Pettersson et al · 2020
Later among the works it cites.
m3di: a program for computing the meromorphic 3D-index
Rafał Siejakowski · 2021
Closest in time.
Infinitesimal gluing equations and the adjoint hyperbolic Reidemeister torsion
Rafał Siejakowski · 2021
Closest in time.
Periods, the meromorphic 3D-index and the Turaev–Viro invariant,
Stavros Garoufalidis and Campbell Wheeler · 2022
Closest in time.
Circle-valued angle structures and obstruction theory
Craig D. Hodgson, Andrew J. Kricker, and Rafael Siejakowski · 2024
Closest in time.