Link homotopy invariants of graphs in R3.
In this paper we define a link homotopy invariant of spatial graphs based on the second degree coefficient of the Conway polynomial of a knot.
Link invariants from finite biracks
A birack is an algebraic structure with axioms encoding the blackboard-framed Reidemeister moves, incorporating quandles, racks, strong biquandles and semiquandles as special cases. In this paper we extend the counting invariant for finite racks to the case of finite biracks. We introduce a family of biracks generalizing Alexander quandles, (t,s)-racks, Alexander biquandles and Silver-Williams switches, known as (τ,σ,ρ)-biracks. We consider enhancements of the counting invariant using writhe vectors,...
Link invariants from finite racks
We define ambient isotopy invariants of oriented knots and links using the counting invariants of framed links defined by finite racks. These invariants reduce to the usual quandle counting invariant when the rack in question is a quandle. We are able to further enhance these counting invariants with 2-cocycles from the coloring rack's second rack cohomology satisfying a new degeneracy condition which reduces to the usual case for quandles.
Link types under twisting solid tori with essencial boundaries.
LinKnot
Links and cycles II: families of commutation relations, parametrized by knots, in the mapping class groups and beyond
We generate families of commutation relations in various groups, by examining quandle colorings of knots and their quandle 2-cycles. The colorings are via quandles associated to the given groups.
Links associated with generic immersions of graphs.
Links of homeomorphisms of a disk and topological entropy.
L'instanton gordien
Lissajous knots and billiard knots
We show that Lissajous knots are equivalent to billiard knots in a cube. We consider also knots in general 3-dimensional billiard tables. We analyse symmetry of knots in billiard tables and show in particular that the Alexander polynomial of a Lissajous knot is a square modulo 2.
Löbell manifolds revised.
Local coordinates for -character varieties of finite-volume hyperbolic 3-manifolds
Given a finite-volume hyperbolic 3-manifold, we compose a lift of the holonomy in with the -dimensional irreducible representation of in . In this paper we give local coordinates of the -character variety around the character of this representation. As a corollary, this representation is isolated among all representations that are unipotent at the cusps.
Local rigidity of aspherical three-manifolds
In this paper we construct, for each aspherical oriented -manifold , a -dimensional class in the -homology of whose norm combined with the Gromov simplicial volume of gives a characterization of those nonzero degree maps from to which are homotopic to a covering map. As an application we characterize those degree one maps which are homotopic to a homeomorphism in term of isometries between the bounded cohomology groups of and .
Localization of group rings and applications to 2-complexes.
Locally unknotted spines of Heegaard splittings.
Longitude Floer homology and the Whitehead double.
L'ordre de Dehornoy sur les tresses