Noncoincidence index, free group actions, and the fixed point property for manifolds (Q919655)

A space X has finite noncoincidence index m if, given maps \(f_ 1,...,f_{m+1}: X\to X\), there exists \(x\in X\) with \(f_ i(x)=f_ j(x)\) for some i, j, but there is a set of m maps without such a coincidence. The main result states that a compact orientable manifold M has finite noncoincidence index if and only if M has nonzero Euler characteristic and admits no fixed point free self-map of degree zero. For such a manifold M, the noncoincidence index is no larger than the sum of the squares of the Betti numbers of M. He investigates the noncoincidence index of M/G where M is simply connected and the finite group G acts freely on M and also discusses the computation of the noncoincidence index for certain classes of homogeneous spaces.