<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"> <mml:msub> <mml:mrow> <mml:mi mathvariant="double-struck">Z</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> </mml:math> -torus actions on positively

Kennard, Khalili Samani, and Searle showed that for a Z 2 -torus, Z 2 r , acting on a closed, positively curved Riemannian n -manifold, M n , with a non-empty fixed point set for n large enough and r approximately half the dimension of M , then M n is homotopy equivalent to S n , R P n , C P n 2 , or a lens space. In this paper, we lower r to approximately 2 n / 5 and show that we still obtain the same result.