  We present Fermi-LAT and multi-frequency, multi-epoch VLBA data for the TeV
blazar Mrk421. We collected the data during a long and intensive
multi-frequency campaign in 2011. We study the gamma-ray light curve, the
photon index evolution and their connection to the radio data on sub-parsec
scales, including total intensity, polarized flux density, polarization angle,
spectral index, and rotation measure both in the core and the jet region. The
VLBA data were obtained at 15 and 24 GHz for 12 epochs and at 43 GHz for 23
epochs, thus providing the best temporal and spatial coverage in the radio band
ever achieved for a TeV blazar. We provide significant constraints on the jet
Doppler factor, the presence of proper motion, the magnetic field
configuration, and an intriguing connection between variability in the radio
data and the gamma-ray light curve: the total intensity and polarized core
emission reach a peak simultaneously to the main gamma-ray peak, followed by a
rotation of the polarization angle at low frequency. Opacity-related, long
wavelength polarization swings are also detected later in the year, possibly
related to secondary peaks in the gamma-ray light curve, setting constraints on
the physics of the gamma-ray zone.
