Some applications of coincidence theory

Summary

As a first application we compute the Lefschetz coincidence number of maps between manifolds$\mathcal{M}$ whose rational singular cohomologyH*$(\mathcal{M};\mathbb{Q})$ has a simple system of generators.

For the second let$\mathcal{M}$ be anH-manifold with multiplicationm. Define for$x \in \mathcal{M}$,m ₂ (x,x)=m(x,x) andm _k (x)=m(x,m _k−1 (x)), for allk>2. All roots of equationm _k (x)=m ₈ (x),k>s such thatm _k (x)=m ₃ (x) butm _i (x)≠m _j (x) for allk>i>j,s≥j≥0 andk−s does not dividei−j, split into a finite number of equivalence classes. We compute precisely the numbers of classes such that their members satisfy the above property.