Abstract:

We introduce the concept of a homotopy motion of a surface embedded in a 3-manifold. This notion arises from various natural problems in 3-manifold theory such as domination of manifold pairs, homotopical behavior of simple loops on a Heegaard surface, and monodromies of virtual branched covering surface bundles associated to a Heegaard splitting. This is joint work with Makoto Sakuma.