The Two-Holed Torus and 3-Crosscaps Surface - Algebraic Topology - NJ Wildberger

Explore the hyperbolic geometric structure of the two-holed torus and 3-crosscaps surface in this advanced algebraic topology lecture. Delve into the process of cutting a two-holed torus into four hexagons and examine the resulting tessellation of the hyperbolic plane using the Beltrami Poincare model. Investigate an octagon model involving the standard form and briefly analyze the 3-crosscaps surface. Gain insights into connected surfaces, tessellations, and hyperbolic geometry as part of a comprehensive beginner's course on Algebraic Topology.

Introduction
Tessellation
Connected surfaces
Four corners
Geometry
Hyperbolic Geometry
Hexagons
Isometry