The RO(ΠB)-graded C₂-equivariant ordinary cohomology of B_C₂ U(1) · arXivDesk
1312.0926Dec 3, 201352 pages. Accepted manuscript; main difference from previous versions is the removal of Part 4 with general results about equivariant cohomology and the calculation of the cohomology of a point and EC_2
The RO(ΠB)-graded C2-equivariant ordinary cohomology of BC2U(1)
We calculate the ordinary C2-cohomology, with Burnside ring coefficients, of CPC2∞=BC2U(1)
Nearby in the stack
, the complex projective space, a model for the classifying space for
C2
-equivariant complex line bundles. The
RO(C2)
-graded Bredon ordinary cohomology was calculated by Gaunce Lewis, but here we extend to a larger grading in order to capture a more natural set of generators. These generators include the Euler class of the tautological bundle, which lies outside of the