Observation and Polarization Measurements of B±→ϕK1± and B±→ϕK2*±

With the full BABAR data sample of 465×106 BB̅ pairs, we observe the decays B±→φK1(1270)± and B±→φK2*(1430)±. We measure the branching fractions (6.1±1.6±1.1)×10-6 and (8.4±1.8±1.0)×10-6 and the fractions of longitudinal polarization 0.46-0.13-0.07+0.12+0.06 and 0.80-0.10+0.09±0.03, respectively. We also report on the B±→φK0*(1430)± decay branching fraction of (7.0±1.3±0.9)×10-6 and several parameters sensitive to CP violation and interference in the above three decays. Upper limits are placed on the B± decay rates to final states with φ and K1(1400)±, K*(1410)±, K2(1770)±, or K2(1820)±. Understanding the observed polarization pattern requires amplitude contributions from an uncertain source.