Nielsen equivalence and multisections of 4-manifolds

Abstract

Islambouli showed that there exist infinitely many 4-manifolds admitting non-isotopic trisections using a Nielsen equivalence, which can be used to construct non-isotopic Heegaard splittings. In this paper, we show that there exist infinitely many 4-manifolds admitting non-isotopic bisections in the same way. Moreover, we show that there exist infinitely many 4-manifolds admitting non-isotopic 4-sections by considering the doubles of the bisections.