Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5777820 | Topology and its Applications | 2017 | 18 Pages |
Abstract
Let f1,...,fk:XâN be maps from a complex X to a compact manifold N, kâ¥2. In previous works [1], [12], a Lefschetz type theorem was established so that the non-vanishing of a Lefschetz type coincidence class L(f1,...,fk) implies the existence of a coincidence xâX such that f1(x)=...=fk(x). In this paper, we investigate the converse of the Lefschetz coincidence theorem for multiple maps. In particular, we study the obstruction to deforming the maps f1,...,fk to be coincidence free. We construct an example of two maps f1,f2:MâT from a sympletic 4-manifold M to the 2-torus T such that f1 and f2 cannot be homotopic to coincidence free maps but for anyf:MâT, the maps f1,f2,f are deformable to be coincidence free.
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
Authors
ThaÃs F.M. Monis, Peter Wong,