On the Mahler measure of Jones polynomials under twisting.
On the Ozsváth-Szabó invariant of negative definite plumbed 3-manifolds.
On the Reidemeister torsion of rational homology spheres.
On the rho invariant for manifolds with boundary.
On the slice genus of links.
On Yetter's invariant and an extension of the Dijkgraaf-Witten invariant to categorical groups.
Orderable 3-manifold groups
We investigate the orderability properties of fundamental groups of 3-dimensional manifolds. Many 3-manifold groups support left-invariant orderings, including all compact -irreducible manifolds with positive first Betti number. For seven of the eight geometries (excluding hyperbolic) we are able to characterize which manifolds’ groups support a left-invariant or bi-invariant ordering. We also show that manifolds modelled on these geometries have virtually bi-orderable groups. The question of virtual orderability...