Jan Jaworowski*
Indiana University, Bloomington, IN, USA
Degrees of maps of free $\bsG$-manifolds
Suppose that $G$ is a compact Lie group, $M$ and $N$ are orientable, connected, smooth, free $G$-manifolds. We show that for certain class of maps $f:M \to N$, including equivariant maps, the degree of $f$ satisfies a formula involving data given by the classifying maps of the orbit spaces $M/G$ and $N/G$. In particular, if $f$ is equivariant, and if the generator of the top dimensional cohomology of $M/G$ with integer coefficients is in the image of the cohomology map induced by the classifying map for $M$, then the degree of $f$ is one. We also study the degree of maps $f:M \to N$ that are ``equivariant up to an exponent'', or equivariant ``up to a homomorphism''.
* This is a joint work with Neľa Mramor-Kosta.
