The Classification of Surfaces with Boundary
نویسنده
چکیده
The classification of surfaces theorem was one of the earliest triumphs of algebraic topology. It states that any closed connected surface is homeomorphic to the sphere, the connected sum of n tori, or the connected sum of m projective planes. This paper begins by defining the geometric, topological, and algebraic tools necessary to understanding the theorem, then proceeds through the technical motivation of the theorem and its proof, and closes with its extension to surfaces with boundary. Along the way, a variety of examples and other pertinent information are provided. Some knowledge of algebraic topology will be helpful.
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