Representation of links by braids: A new algorithm.
Representations in SU(2) of the fundamental groups of the Whitehead link and of doubled knots.
Representations of (1,1)-knots
We present two different representations of (1,1)-knots and study some connections between them. The first representation is algebraic: every (1,1)-knot is represented by an element of the pure mapping class group of the twice punctured torus PMCG₂(T). Moreover, there is a surjective map from the kernel of the natural homomorphism Ω:PMCG₂(T) → MCG(T) ≅ SL(2,ℤ), which is a free group of rank two, to the class of all (1,1)-knots in a fixed lens space. The second representation is parametric: every...
Representations of orbifold groups and parabolic bundles.
Representations of palindromically presented groups onto finite subgroups of
Representations of polygons of finite groups.
Representations of the Kauffman bracket skein algebra of the punctured torus
We describe the action of the Kauffman bracket skein algebra on some vector spaces that arise as relative Kauffman bracket skein modules of tangles in the punctured torus. We show how this action determines the Reshetikhin-Turaev representation of the punctured torus. We rephrase our results to describe the quantum group quantization of the moduli space of flat SU(2)-connections on the punctured torus with fixed trace of the holonomy around the boundary.
Representations of the Whitehead manifold and Julia sets
Representing 3-manifolds by triangulations of . I: A constructive approach.
Representing open 3-manifolds as 3-fold branched coverings.
It is proved that the Freudenthal compactification of an open, connected, oriented 3-manifold is a 3-fold branched covering of S3, and in some cases, a 2-fold branched covering of S3. The branching set is a locally finite disjoint union of strings.
Reshetikhin-Turaev invariants of Seifert 3-manifolds and a rational surgery formula.
Residual Finiteness of Surface Groups via Tessellations.
Resolutions of moduli spaces and homological stability
We describe partial semi-simplicial resolutions of moduli spaces of surfaces with tangential structure. This allows us to prove a homological stability theorem for these moduli spaces, which often improves the known stability ranges and gives explicit stability ranges in many new cases. In each of these cases the stable homology can be identified using the methods of Galatius, Madsen, Tillmann and Weiss.
Resurgence of the Kontsevich-Zagier series
The paper is concerned with the resurgence of the Kontsevich-Zagier seriesWe 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. We also prove that the...
Ribbon Concordance of Knots in the 3-Sphere.
Ribbon knots of 1-fusion, the Jones polynomial, and the Casson-Walker invariant.
We give an explicit formula for the Casson-Walker invariant of double branched covers of S3 branched along ribbon knots of 1-fusion.
Rigid sets in manifolds
Rigidity of cusps in deformations of hyperbolic 3-orbifolds.
Roots and Centralizers of Peripheral Elements in Knot Groups.
Rotary hypermaps of genus 2.