Minimal set of periods for continuous self-maps of the eight space

MTM2016-77278-P grant 2017SGR1617 grant MSCA-RISE-2017-777911Let Gk be a bouquet of circles, i.e., the quotient space of the interval [ 0 , k] obtained by identifying all points of integer coordinates to a single point, called the branching point of Gk. Thus, G1 is the circle, G2 is the eight space, and G3 is the trefoil. Let f: Gk→ Gk be a continuous map such that, for k> 1 , the branching point is fixed. If Per (f) denotes the set of periods of f, the minimal set of periods of f, denoted by MPer (f) , is defined as ⋂ g≃fPer (g) where g: Gk→ Gk is homological to f. The sets MPer (f) are well known for circle maps. Here, we classify all the sets MPer (f) for self-maps of the eight space.publishersversionpublishe