It was recently revealed that a rotating compact body responds dynamically when it is subjected to a gravitomagnetic tidal field, even when this field is idealized as time-independent. The dynamical response is characterized by time-changing internal currents, and it was suspected to originate from zero-frequency g-modes and r-modes driven by the tidal forces. In this paper we provide additional insights into the phenomenon by examining the tidal response of a rotating body within the framework of post-Newtonian gravity. This approach allows us to develop an intuitive picture for the phenomenon, which relies on the close analogy between post-Newtonian gravity and Maxwell's theory of electromagnetism. In this picture, the coupling between the gravitomagnetic tidal field and the body's rotational velocity is naturally expected to produce an unbalanced Lorentz-like force within the body, and it is this force that is responsible for the tidal currents. The simplicity of the fluid equations in the post-Newtonian setting allows us to provide a complete description of the zero-frequency modes and demonstrate their precise role in the establishment of the tidal currents. We estimate the amplitude of these currents, and find that for neutron-star binaries of relevance to LIGO, the scale of the velocity perturbation is measured in kilometers per second when the rotation period is comparable to 100 milliseconds. This estimate indicates that the tidal currents may have a significant impact on the physics of neutron stars near merger.Comment: 24 pages, 3 figures, final version to be published in Physical Review

We define a diagram associated to any algebraic connection on a vector bundle on a Zariski open subset of the Riemann sphere, generalizing previous constructions to the case when there are several irregular singularities. The construction relies on applying the Fourier-Laplace transform to reduce to the case where there is only one irregular singularity at infinity, and then using the definition of Boalch-Yamakawa in that case. We prove the diagram is invariant under the symplectic automorphisms of the Weyl algebra, so that there are several readings of the same diagram corresponding to connections with different formal data, usually on different rank bundles.

We will define and study some generalisations of pure g-braid groups that occur in the theory of connections on curves, for any complex reductive Lie algebra g. They make up local pieces of the wild mapping class groups, which are fundamental groups of (universal) deformations of wild Riemann surfaces, underlying the braiding of Stokes data and generalising the usual mapping class groups. We will establish a general product decomposition for the local wild mapping class groups, and in many cases define a fission tree controlling this decomposition. Further in type A we will show one obtains cabled versions of braid groups, related to braid operads.

We will define and study moduli spaces of deformations of irregular classes on Riemann surfaces, which provide an intrinsic viewpoint on the ‘times’ of irregular isomonodromy systems in general. Our aim is to study the deeper generalisation of the G-braid groups that occur as fundamental groups of such deformation spaces, with particular focus on the generalisation of the full G-braid groups.