Cohomology Algebra of Orbit Spaces of Free Involutions on Lens Spaces
نویسنده
چکیده
We determine the possible cohomology algebra of orbit space of any free involution on a mod-2 cohomology lens space X using the Leray spectral sequence associated to the Borel fibration X →֒ XZ2 −→ BZ2 . As an application we show that if X is a mod-2 cohomology lens space of dimension 2m − 1 where 4 ∤ m, then there does not exist any Z2-equivariant map S n → X for n ≥ 2, where S is equipped with the antipodal involution.
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