Functions on surfaces and constructions of 3-, 4- and 5-manifolds

I'll steal ideas from Lickorish's proof that 3-manifolds bound 4-manifolds and Hatcher and Thurston's proof that the mapping class group of a surface is finitely presented to give, among other things, a new proof that $\Omega_4=\mathbb{Z}$ (using trisections where Lickorish uses Heegaard splittings). The key idea is that generic $n$-parameter families of functions on surfaces describe  $(n+3)$-manifolds, at least for $n\leq 2$.