Partial-Wave Analysis of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>3</mml:mn><mml:mi>π</mml:mi></mml:math>Decay of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>

A new partial-wave analysis is applied to the $3\ensuremath{\pi}$ decay of the ${{A}_{2}}^{\ensuremath{-}}$ in the reaction ${\ensuremath{\pi}}^{\ensuremath{-}}p\ensuremath{\rightarrow}p{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{\ensuremath{-}}$ at 5 and 7.5 $\frac{\mathrm{GeV}}{c}$. The relative importance of the spins and parities ${0}^{\ensuremath{-}}$, ${1}^{+}$, ${1}^{\ensuremath{-}}$, ${2}^{+}$, and ${2}^{\ensuremath{-}}$ are obtained as a function of $3\ensuremath{\pi}$ mass. Only the ${2}^{+}$ spin and parity shows resonant structure. Results are also given on the polarization and momentum-transfer dependence of the ${A}_{2}$ and on the mass dependence of the interference of ${1}^{+}$ background with ${2}^{+}$ resonance.