arXiv subjects
Publications and source records attributed to Leslie Mavrakis.
We show that there is a universal compact branched 3-manifold $W$ such that a closed 3-manifold $M$ immerses into $W$ if and only if $M$ admits a Sol structure. Equivalently, a closed 3-manifold is Sol if and only if it has a certain type of triangulation. The construction of $W$ is based on a regular language that characterizes Sol manifolds.
A family of compact n-manifolds is locally combinatorially defined (LCD) if it can be specified by a finite number of local triangulations. We show that LCD is equivalent to the existence of a compact branched n-manifold W, such that the family is precisely those manifolds that immerse into W. In subsequent papers, the equivalence will be used to show that, for each of the eight Thurston geometries, the family of closed 3-manifolds admitting that geometry is LCD.
A braided fusion category is said to have Property $\textbf{F}$ if the associated braid group representations factor over a finite group. We verify integral metaplectic modular categories have property $\textbf{F}$ by showing these categories are group theoretical. For the special case of integral categories $\mathcal{C}$ with the fusion rules of $SO(8)_2$ we determine the finite group $G$ for which $Rep(D^ωG)$ is braided equivalent to $\mathcal{Z}(\mathcal{C})$. In addition, we determine the associated classical link invariant, an evaluation of the 2-variable Kauffman polynomial at a point.