Pachner move and affine volume-preserving geometry in .
Parity biquandle
We use crossing parity to construct a generalization of biquandles for virtual knots which we call parity biquandles. These structures include all biquandles as a standard example referred to as the even parity biquandle. We find all parity biquandles arising from the Alexander biquandle and quaternionic biquandles. For a particular construction named the z-parity Alexander biquandle we show that the associated polynomial yields a lower bound on the number of odd crossings as well as the total number...
Patterns in knot cohomology. I.
Plane curve singularities and carousels
In this paper we give a direct and explicit description of the local topological embedding of a plane curve singularity using the Puiseux expansions of its branches in a given set of coordinates.
Polynomial invariants of links in the projective space
The Homflypt and Kauffman skein modules of the projective space are computed. Both are free and generated by some infinite set of links. This set may be chosen to be {Lₙ: n ∈ ℕ ∪ {0}}, where Lₙ is an arbitrary link consisting of n projective lines for n > 0, and L₀ is an affine unknot.
Pure virtual braids homotopic to the identity braid
Two virtual link diagrams are homotopic if one may be transformed into the other by a sequence of virtual Reidemeister moves, classical Reidemeister moves, and self crossing changes. We recall the pure virtual braid group. We then describe the set of pure virtual braids that are homotopic to the identity braid.