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We present four high dynamic range, dual-circular polarization, Very Long Baseline Array (VLBA) observations at 22 GHz of Mrk 421, taken throughout the year following the source's unprecedented gamma-ray high state in early 2001. Previous VLBI observations of this source had shown only subluminal apparent motions in the parsec-scale jet and no apparent connection between jet components and gamma-ray flares, so we examined whether the larger gamma-ray flares of 2001 had produced a component that could be followed on the parsec-scale VLBA images. These four new VLBA observations are combined with data from our earlier 1999 paper and archival VLBA data sets that have become available since 1999 to produce a combined 28 epoch VLBA data set on Mrk 421 spanning 1994-2002. No new component associated with the 2001 flares was seen on the total intensity images, but the combined data set allowed precise measurements of the apparent speeds of the existing components. The peak measured apparent speed was for component C5, which has an apparent speed of 0.1c ± 0.02c (H0 = 71 km s-1 Mpc-1, Ωm = 0.27, and ΩΛ = 0.73). No counterjet is seen with a limit on the jet to counterjet brightness ratio J >~ 100. These observed VLBI properties of Mrk 421 are consistent with a jet with a bulk Lorentz factor Γ ~ 2 and an angle to the line of sight θ ~ 1°, suggesting a jet that decelerates between the gamma-ray producing region and the parsec scale. Although a limb-brightened structure is seen in some transverse slices across the jet, it is not seen consistently, inhibiting interpretation in terms of the fast-spine/slow-layer model that has been invoked for other sources. The VLBI core and inner jet (component C7) have fractional polarizations of ~5% and an electric vector position angle (EVPA) aligned with the jet axis. Component C5 (at 1.5 mas from the core) has a higher fractional polarization of ~15% and an EVPA nearly orthogonal to the jet axis. Significant variability is detected in the EVPA of component C6, which at two of the four epochs shows an EVPA aligned with the jet axis, possibly a sign of propagating disturbances that are only visible on the polarization images. If these propagating disturbances are linked to the 2001 gamma-ray high state, then their inferred apparent speed is between 1c and 3c.

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