  Momentum-space curvature, which is expected in some approaches to the
quantum-gravity problem, can produce dual redshift, a feature which introduces
energy dependence of the travel times of ultrarelativistic particles, and dual
lensing, a feature which mainly affects the direction of observation of
particles. In our recent arXiv:1605.00496 we explored the possibility that dual
redshift might be relevant in the analysis of IceCube neutrinos, obtaining
results which are preliminarily encouraging. Here we explore the possibility
that also dual lensing might play a role in the analysis of IceCube neutrinos.
In doing so we also investigate issues which are of broader interest, such as
the possibility of estimating the contribution by background neutrinos and some
noteworthy differences between candidate "early neutrinos" and candidate "late
neutrinos".
