6 papers
The 27 possible intrinsic symmetry groups of two-component links
Jason Cantarella, James Cornish, Matt Mastin +1
We consider the "intrinsic" symmetry group of a two-component link , defined to be the image of the natural homomorphism from the standard symmetry group $\MCG(S^3,L)$ to…
A geometric and combinatorial view of weighted voting
Sarah Mason, Jason Parsley
A natural partial ordering exists on the set of all weighted games and, more broadly, on all linear games. We describe several properties of the partially ordered sets formed by th…
An infinite family of convex Brunnian links in
Robert Davis, Hugh Howards, Jonathan Newman +1
This paper proves that convex Brunnian links exist for every dimension by constructing explicit examples. These examples are three-component links which are higher-dimen…
Intrinsic symmetry groups of links with 8 and fewer crossings
Michael Berglund, Jason Cantarella, Meredith Perrie Casey +9
We present an elementary derivation of the "intrinsic" symmetry groups for knots and links of 8 or fewer crossings. The standard symmetry group for a link is the mapping class grou…
The Biot-Savart operator and electrodynamics on subdomains of the three-sphere
Jason Parsley
We study steady-state magnetic fields in the geometric setting of positive curvature on subdomains of the three-dimensional sphere. By generalizing the Biot-Savart law to an integr…
A new cohomological formula for helicity in reveals the effect of a diffeomorphism on helicity
Jason Cantarella, Jason Parsley
The helicity of a vector field is a measure of the average linking of pairs of integral curves of the field. Computed by a six-dimensional integral, it is widely useful in the phys…