Line Bundles over Framed Manifolds.
Line Fields with Branch Defects.
Linear representations of the group of conjugating automorphisms and the braid groups of some manifolds.
Link bordism skein modules
We compute link bordism skein modules of colored oriented links in oriented 3-manifolds. A Hurewicz theorem relating link bordism and link homotopy skein modules is proved.
Link concordance and algebraic closure, II.
Link concordance, homology cobordism, and Hirzebruch-type defects from iterated p-covers
Link concordance implies link homotopy.
Link concordance invariants and homotopy theory.
Link genus and the Conway moves.
Link homology and Frobenius extensions
We explain how rank two Frobenius extensions of commutative rings lead to link homology theories and discuss relations between these theories, Bar-Natan theories, equivariant cohomology and the Rasmussen invariant.
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.