A conjecture on Khovanov's invariants
We formulate a conjectural formula for Khovanov's invariants of alternating knots in terms of the Jones polynomial and the signature of the knot.
On finite type 3-mainfold invarinats II.
Resurgence of the Euler-MacLaurin summation formula
The Euler-MacLaurin summation formula compares the sum of a function over the lattice points of an interval with its corresponding integral, plus a remainder term. The remainder term has an asymptotic expansion, and for a typical analytic function, it is a divergent (Gevrey-1) series. Under some decay assumptions of the function in a half-plane (resp. in the vertical strip containing the summation interval), Hardy (resp. Abel-Plana) prove that the asymptotic expansion is a Borel summable series,...
Resurgence of the Kontsevich-Zagier series
The paper is concerned with the resurgence of the Kontsevich-Zagier series We give an explicit formula for the Borel transform of the power series when from which its analytic continuation, its singularities (all on the positive real axis) and the local monodromy can be manifestly determined. We also give two formulas (one involving the Dedekind eta function, and another involving the complex error function) for the right, left and median summation of the Borel transform....
Whitehead doubling persists.
A rational noncommutative invariant of boundary links.
Homology surgery and invariants of 3-manifolds.
Concordance and 1-loop clovers.
Experimental evidence for the Volume Conjecture for the simplest hyperbolic non-2-bridge knot.
Non-triviality of the -polynomial for knots in .
The A-polynomial of the pretzel knots.
Calculus of clovers and finite type invariants of 3-manifolds.
The colored Jones function is -holonomic.
Behavior of knot invariants under genus 2 mutation.
Analyticity of the free energy of a closed 3-manifold.
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