Parametrized Borsuk-Ulam problem for projective space bundles
Mahender Singh
Fundamenta Mathematicae, Tome 215 (2011), p. 135-147 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

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 Zf=x∈E|f(x)=0. As an application, we also estimate the cohomological dimension of the ℤ₂-coincidence set Af=x∈E|f(x)=f(T(x)) of a fiber preserving map f: E → E’.

Publié le : 2011-01-01
EUDML-ID : urn:eudml:doc:282703 
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm211-2-2,
     author = {Mahender Singh},
     title = {Parametrized Borsuk-Ulam problem for projective space bundles},
     journal = {Fundamenta Mathematicae},
     volume = {215},
     year = {2011},
     pages = {135-147},
     zbl = {1220.55002},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm211-2-2}
}

Mahender Singh. Parametrized Borsuk-Ulam problem for projective space bundles. Fundamenta Mathematicae, Tome 215 (2011) pp. 135-147. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm211-2-2/