Abstract
Frontiers in geometry and topology, Proc. Sympos. Pure Math., 109,
71--98, (2024) Amer. Math. Soc., Providence, RI We construct a number of topologically trivial but smoothly non-trivial
families of embeddings of 3-manifolds in 4-manifolds. These include embeddings
of homology spheres in $S^4$ that are not isotopic but have diffeomorphic
complements, and families (parameterized by high-dimensional spheres) of
embeddings of any 3-manifold that embeds in a blown-up K3 surface. In each
case, the families are constructed so as to be topologically trivial in an
appropriate sense. We also illustrate a general technique for converting a
non-trivial family of embeddings into a non-trivial family of submanifolds.