  We investigate the impact of AGN feedback on the gravitational lensing
properties of a sample of galaxy clusters with masses in the range 10^14 -
10^15 Msol, using state-of-the-art simulations. Adopting a ray-tracing
algorithm, we compute the cross-section of giant arcs from clusters simulated
with dark-matter only physics (DM), dark matter plus gas with cooling and star
formation (CSF), and dark matter plus gas with cooling, star formation and AGN
feedback (CSFBH). Once AGN feedback is included, baryonic physics boosts the
strong lensing cross-section by much less than previously estimated using
clusters simulated with only cooling and star formation. For a cluster with a
virial mass of 7.4 X 10^14 Msol, inclusion of baryonic physics without feedback
can boost the cross-section by as much as a factor of 3, in agreement with
previous studies, whereas once AGN feedback is included this maximal figure
falls to a factor of 2 at most. Typically, clusters simulated with DM and CSFBH
physics have similar cross-sections for the production of giant arcs. We also
investigate how baryonic physics affects the weak lensing properties of the
simulated clusters by fitting NFW profiles to synthetic weak lensing data sets
using a Markov Chain Monte Carlo approach, and by performing non-parametric
mass reconstructions. Without the inclusion of AGN feedback, measured
concentration parameters can be much larger than those obtained with AGN
feedback, which are similar to the dark-matter only case.
