A CATEGORICAL MODEL FOR THE VIRTUAL BRAID GROUP

Categorical Affine Braid Group Action on Springer Resolutions

investigating the feasibility of a proposed model for geometric design of deployable arch structures

deployable scissor type structures are composed of the so-called scissor-like elements (sles), which are connected to each other at an intermediate point through a pivotal connection and allow them to be folded into a compact bundle for storage or transport. several sles are connected to each other in order to form units with regular polygonal plan views. the sides and radii of the polygons are...

Anyonic Topological Quantum Computation and the Virtual Braid Group

We introduce a recoupling theory for virtual braided trees. This recoupling theory can be utilized to incorporate swap gates into anyonic models of quantum computation. 1 Classical Trees Louis Kauffman and Sam Lomonaco reconstructed the Fibonacci model of quantum computation in [7] by applying the 2-strand Temperly-Lieb recoupling and the skein relation to braided trees. (The original Fibonacci...

Generators for a Complex Hyperbolic Braid Group

We give generators for a certain complex hyperbolic braid group. That is, we remove a hyperplane arrangement from complex hyperbolic 13space, take the quotient of the remaining space by a discrete group, and find generators for the orbifold fundamental group of the quotient. These generators have the most natural form: loops corresponding to the hyperplanes which come nearest the basepoint. Our...

On a Braid Group Action

We discuss some consequences of the braid group action on a categorified quantum group. Results include a description of reflection functors for quiver Hecke algebras and a theory of restricting categorical representations along a face.