Year: 1963
Type: article
Abstract: In the following, a surface is always a compact, orientable, twodimensional manifold with or without boundary, a closed surface is one without boundary, and a simple, closed curve on a surface is a closed, connected, one-dimensional submanifold. For simplicity in referring to curves, no notational distinction is made between the embedding of the circle and the image under the embedding-the context will make it clear which is intended. If W is a surface whose boundary consists of n disjoint, simple, closed curves, the genus of W, g(W), is defined to be the genus of a surface without boundary obtained by attaching a 2-cell to each of the boundary curves. The relation between the genus of W and its inner Euler characteristic, x(W) is:
Author: Harold I. Levine
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W1964783572