Adam Howard's PhD Thesis Defense, "Spaces of Immersions and their Homotopy Groups"
- Monday, November 29, 2021 from 4:10pm to 5:15pm
- Wilson Hall, 1-143 - view map
PhD Thesis Defense
Monday, November 29, 4:10-5:15pm MT
Wilson Hall 1-143
Adam Howard (Montana State University)
Spaces of Immersions and their Homotopy Groups
If you have ever seen a model of a Klein bottle, this is an immersion of a closed non-orientable surface into 3-dimensional Euclidean space. The set of all immersions from one manifold into another can be equipped with a topology and analyzing the connected components of this space allows us to distinguish immersions up to regular homotopy. In this talk, we will identify the connected components, as well as the higher homotopy groups, of the space of immersions from a closed orientable surface into an arbitrary parallelizable manifold. An application of this work is that every immersion of a 2-torus into a hyperbolic manifold is regularly homotopic to a self-cover of a tubular neighborhood of some closed geodesic.
- Department of Mathematical Sciences