Surfaces in Three- and Four-Dimensional Topology
We investigate two ways in which a surface embedded or immersed in a manifold can reveal information about topology of the ambient space. In particular, we prove a special case of the Simple Loop Conjecture for 3-Manifolds and the study trisections of 4-manifolds from the perspectives of the mapping class group and the curve complex of a surface.
Manning, Jason F.
Holm, Tara S.; Riley, Timothy R.
Ph. D., Mathematics
Doctor of Philosophy
dissertation or thesis