### AlgTop21: The two-holed torus and 3-crosscaps surface

We describe how the two-holed torus and the 3-crosscaps surface can be given hyperbolic geometric structure. For the two-holed torus we cut it into 4 hexagons and then describe a tesselation of the hyperbolic plane (using the Beltrami Poincare model described in the previous lecture) composed of regular hexagons meeting four at a vertex. We will look at an octagon model involving the standard form. Then we briefly look at the 3-crosscaps surface in the same way.This is the 21st lecture in this beginner's course on Algebraic Topology, given by N J Wildberger of UNSW.

Length:
38:53