260 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
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
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
Symmetric continuous cohomology of topological groups
In this paper, we introduce a symmetric continuous cohomology of topological
groups. This is obtained by topologizing a recent construction due to Staic (J.
Algebra 322 (2009), 1360-1378), where a symmetric cohomology of abstract groups
is constructed. We give a characterization of topological group extensions that
correspond to elements of the second symmetric continuous cohomology. We also
show that the symmetric continuous cohomology of a profinite group with
coefficients in a discrete module is equal to the direct limit of the symmetric
cohomology of finite groups. In the end, we also define symmetric smooth
cohomology of Lie groups and prove similar results.Comment: 23 pages, to appear in Homology Homotopy and Application
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