Higher gauge theory is a higher order version of gauge theory that makes possible the
definition of 2-dimensional holonomy along surfaces embedded in a manifold where a …

In topological quantum computing, information is encoded in “knotted” quantum states of
topological phases of matter, thus being locked into topology to prevent decay. Topological …

In this paper we introduce distinct approaches to loop braid groups, a generalization of braid
groups, and unify all the definitions that have appeared so far in the literature, with a …

We propose an exactly solvable Hamiltonian for topological phases in 3+ 1 dimensions
utilizing ideas from higher lattice gauge theory, where the gauge symmetry is given by a …

We show that representations of the loop braid group arise from Aharonov-Bohm like effects
in finite 2-group (3+ 1)-dimensional topological higher gauge theory. For this we introduce a …

Unrestricted virtual braids, fused links and other quotients of virtual braid groups Page 1 Journal
of Knot Theory and Its Ramifications Vol. 24, No. 12 (2015) 1550063 (23 pages) c© World …

The necklace braid group NB _n NB n is the motion group of the n+ 1 n+ 1 component
necklace link L _n L n in Euclidean R^ 3 R 3. Here L _n L n consists of n pairwise unlinked …

Given a fully extended topological quantum field theory, the “crossing with the circle”
conditions establish that the dimension, or categorification thereof, of the quantum invariant …

Two-dimensional topological states of matter offer a route to quantum computation that
would be topologically protected against the nemesis of the quantum circuit model …

Here a loop braid representation is a monoidal functor F from the loop braid category L to a
suitable target category, and is N-charge-conserving if the target is the category Match N of …