575 research outputs found
Parametrized Borsuk-Ulam problem for projective space bundles
Let be a fiber bundle with fiber having the mod 2 cohomology
algebra of a real or a complex projective space and let
be vector bundle such that acts fiber preserving and freely on
and , where 0 stands for the zero section of the bundle
. For a fiber preserving -equivariant map
, we estimate the cohomological dimension of the zero set As an application, we also estimate the cohomological
dimension of the -coincidence set of a fiber preserving map .Comment: 14 pages, to appear in Fundamenta Mathematica
Z_2 actions on complexes with three non-trivial cells
In this paper, we study actions on a cell complex X having the
cohomology ring isomorphic to that of the wedge sum or . We determine the possible fixed point sets depending on
whether or not X is totally non-homologous to zero in and give
examples realizing the possible cases.Comment: 7 pages, appeared in Topology and its Application
A note on the commutativity of inverse limit and orbit map
We show that the inverse limit and the orbit map commute for actions of
compact groups on compact Hausdorff spaces.Comment: 4 page
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