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12 papers · 1 filter
On the Volume Conjecture for Cables of Knots
Thang T. Q. Le, Anh T. Tran
We establish the volume conjecture for (m,2)-cables of the figure 8 knot, when m is odd. For (m,2)-cables of general knots where m is even, we show that the limit in the volume con…
The Kontsevich integral and re-normalized link invariants arising from Lie superalgebras
Nathan Geer
We show that the coefficients of the re-normalized link invariants of the paper "Multivariable link invariants arising from Lie superalgebras of type I" are Vassiliev invariants wh…
Analyticity of the Free Energy of a Closed 3-Manifold
Stavros Garoufalidis, Thang T. Q. Le, Marcos Marino
The free energy of a closed 3-manifold is a 2-parameter formal power series which encodes the perturbative Chern-Simons invariant (also known as the LMO invariant) of a closed 3-ma…
The non-commutative -polynomial of twist knots
Stavros Garoufalidis, Xinyu Sun
The purpose of the paper is two-fold: to introduce a multivariable creative telescoping method, and to apply it in a problem of Quantum Topology: namely the computation of the non-…
Grid Diagrams for Lens Spaces and Combinatorial Knot Floer Homology
Kenneth L. Baker, J. Elisenda Grigsby, Matthew Hedden
Similar to knots in S^3, any knot in a lens space has a grid diagram from which one can combinatorially compute all of its knot Floer homology invariants. We give an explicit descr…
Twisted Alexander polynomial of links in the projective space
Vu Q. Huynh, Thang T. Q. Le
We use Reidemeister torsion to study a twisted Alexander polynomial, as defined by Turaev, for links in the projective space. Using sign-refined torsion we derive a skein relation…