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Parametrized Borsuk-Ulam problem for projective space bundles

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Singh M.

Fundamenta Mathematicae

2011

tom 211

nr 2

135-147

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 map f: E → E'.

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1 Fundamenta Mathematicae

1 Singh M.

1 2011

Wyniki wyszukiwania

Parametrized Borsuk-Ulam problem for projective space bundles