We show that the Kakimizu complex of a knot may be locally infinite, answering a question of Przytycki–Schultens. We then prove that if a link only has connected Seifert surfaces and has a locally infinite Kakimizu complex then is a satellite of either a torus knot, a cable knot or a connected sum, with winding number 0.
"On links with locally infinite Kakimizu complexes." Algebr. Geom. Topol. 11 (3) 1445 - 1454, 2011. https://doi.org/10.2140/agt.2011.11.1445