Some applications of coincidence theory

Abstract

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.