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Parametrized Borsuk-Ulam problem for projective space bundles

Mahender Singh (2011)

Fundamenta Mathematicae

Let π: E → B be a fiber bundle with fiber having the mod 2 cohomology algebra of a real or a complex projective space and let π’: E’ → B be a vector bundle such that ℤ₂ acts fiber preserving and freely on E and E’-0, where 0 stands for the zero section of the bundle π’: E’ → B. For a fiber preserving ℤ₂-equivariant map f: E → E’, we estimate the cohomological dimension of the zero set Z f = x E | f ( x ) = 0 . As an application, we also estimate the cohomological dimension of the ℤ₂-coincidence set A f = x E | f ( x ) = f ( T ( x ) ) of a fiber preserving...

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