## Vertex Minimal Immersions of Simplicial Surfaces into 3-Space |

October 28, 1996

3:30 pm

Bailey Hall 201

Refreshments in the common room at 3:15

This talk will descibe some results from my Ph.D. thesis which centered around determining immersions of surfaces that have the fewest possible number of vertices. We will concentrate on the Klein bottle, which can be triangluated using only 8 vertices, but cannot be immersed in 3-space with fewer than 9 vertices. We will begin by showing that there are 9-vertex immersions of the Klein bottle in each of its immersion homotopy classes. To prove that no 8-vertex immersion exists, we will first determine all possible 8-vertex immersions, then will use topological and geometric arguments to show that none can be immersed in space. Physical models of the immersions will be presented to make the talk more concrete.

For additional information, send e-mail to math@union.edu or call (518) 388-6246.

Union College Math Department Home PageComments to: math@union.edu Created automatically on: Tue Oct 23 15:59:42 EDT 2018 |