Parametrized Borsuk-ulam Problem for Projective Space Bundles
نویسنده
چکیده
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 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 Zf = {x ∈ E | f(x) = 0}. As an application, we also estimate the size 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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