Math 554: Foundations of Topology 2

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Catalog Information


Foundations of Topology 2.

(Credit Hours:Lecture Hours:Lab Hours)



Math 553 or instructor's consent.


Fundamental group, retractions and fixed points, homotopy types, separation theorems, classification of surfaces, Seifert-van Kampen Theorem, classification of covering spaces, and applications to group theory.

Desired Learning Outcomes

Students should gain a familiarity with surfaces, fundamental group, and covering spaces.

Minimal learning outcomes

  1. The Fundamenatal Group
  2. The topology of the plane
    • Jordan Curve Theorem
  3. Seifert-van Kampen Theorem
  4. Classification of Surfaces
  5. Classification of Covering Spaces
  6. Group Theory
    • Free groups
    • Free abelian groups
    • Presentations of groups
    • Subgroups of free groups


Possible textbooks for this course include (but are not limited to):

Additional topics

Courses for which this course is prerequisite