University · Mathematics · Topology

Quotient Spaces and the Classification of Surfaces

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Quotient spaces defined via an equivalence relation and the quotient topology, worked examples such as building a circle from an interval and a torus or Klein bottle from a square, the classification theorem for compact surfaces (sphere, connected sums of tori, connected sums of projective planes), and the Euler characteristic as the classifying invariant.

Inhaltsübersicht

  • Quotient Spaces: Gluing via an Equivalence Relation
  • Building Surfaces by Identifying Edges of a Square
  • The Classification Theorem for Compact Surfaces
  • The Euler Characteristic as a Classifying Invariant
A line segment with its two endpoints glued together to form a circle, illustrating a quotient map
Pixabay – Pixabay License

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