Orbit Spaces of Free Involutions on the Product of Two Projective Spaces

作者：Singh Mahender^*

来源：Results in Mathematics, 2010, 57(1-2): 53-67.

DOI：10.1007/s00025-009-0014-8

• Cohomology algebra
• finitistic space
• index of involution
• Leray spectral sequence

Let X be a finitistic space having the mod 2 cohomology algebra of the product of two projective spaces. We study free involutions on X and determine the possible mod 2 cohomology algebra of orbit space of any free involution, using the Leray spectral sequence associated to the Borel fibration X hooked right arrow X(Z2) -> B(Z2). We also give an application of our result to show that if X has the mod 2 cohomology algebra of the product of two real projective spaces (respectively, complex projective spaces), then there does not exist any Z(2)-equivariant map from S(k) -> X for k >= 2 (respectively, k >= 3), where S(k) is equipped with the antipodal involution.

• 出版日期2010-3
• 单位常州工学院