Abstract
We prove that 2 r + 1 ⋅ π ∗ ( P m ( 2 r ) ) = 0 provided m ≥ 4 and r ≥ 6 . This is the best possible result. As well, for 2 ≤ r ≤ 5 we obtain upper bounds on the homotopy exponent of P m ( 2 r ) .
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