Classification of Surfaces

  title={Classification of Surfaces},
  author={CHEN HUI GEORGE},
  • Published 2011
The sphere, torus, Klein bottle, and the projective plane are the classical examples of orientable and non-orientable surfaces. As with much of mathematics, it is natural to ask the question: are these all possible surfaces, or, more generally, can we classify all possible surfaces? In this paper, we examine a result originally due to Seifert and Threlfall that all compact surfaces are homeomorphic to the sphere, the connect sum of tori, or the connect sum of projective planes; for this paper… CONTINUE READING