In this talk I will present some elementary computations in
equivariant (Bredon) homology and cohomology. First I will give a
brief introduction to equivariant homotopy theory and Bredon
(co)homology. For the computations we will focus on the case of a
cyclic group G and constant coefficients Z. We will compute the
equivariant (co)homology of the one point compactification of any
finite dimensional real G-representation. Non-equivariantly these
spaces are just spheres, but their Bredon (co)homology groups will
usually have torsion. The direct sum operation on representations
induces a product in the 'RO(G)-graded' theory. Under this product we
will see that these computations can be unified in an elegant way.
Links:
[1] https://www.mpim-bonn.mpg.de/de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/de/node/3444
[3] https://www.mpim-bonn.mpg.de/de/node/249