Parametrized Borsuk-Ulam problem for projective space bundles

• Autorzy: Mahender Singh
• Języki publikacji: EN

Abstrakty

EN

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'.

Kategorie tematyczne

• 55M20: Fixed points and coincidences
• 55R25: Sphere bundles and vector bundles
• 55M35: Finite groups of transformations (including Smith theory)
• 55M10: Dimension theory
• 55R91: Equivariant fiber spaces and bundles

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2011
• Tom: 211
• Numer: 2
• Strony: 135-147

Daty

wydano

2011

Twórcy

autor

Mahender Singh

• Institute of Mathematical Sciences, C I T Campus, Taramani, Chennai 600113, India

Identyfikatory

DOI

10.4064/fm211-2-2