A sphere with 8 handles
The theorem of classification of the surfaces states that any compact, connected, orientable surface without boundary can be related to a standard surface. We can visualize these standard surfaces as spheres with some handles attached. In the figure, we see an example with 8 handles and it is easy to imagine spheres with a smaller number of handles. Otherwise, another equivalent standard shape is a doughnut with a certain number of holes.
© matematita
The image belongs to the sections...:
Standard surfaces (Topology)
Other surfaces (Topology)
