Parametrized Borsuk-Ulam problem for projective space bundles

Mahender Singh. "Parametrized Borsuk-Ulam problem for projective space bundles." Fundamenta Mathematicae 211.2 (2011): 135-147. <http://eudml.org/doc/282703>.

@article{MahenderSingh2011,
abstract = {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’.},
author = {Mahender Singh},
journal = {Fundamenta Mathematicae},
keywords = {cohomological dimension; zero set},
language = {eng},
number = {2},
pages = {135-147},
title = {Parametrized Borsuk-Ulam problem for projective space bundles},
url = {http://eudml.org/doc/282703},
volume = {211},
year = {2011},
}

TY - JOUR
AU - Mahender Singh
TI - Parametrized Borsuk-Ulam problem for projective space bundles
JO - Fundamenta Mathematicae
PY - 2011
VL - 211
IS - 2
SP - 135
EP - 147
AB - 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’.
LA - eng
KW - cohomological dimension; zero set
UR - http://eudml.org/doc/282703
ER -