Lie Groups pp 146-149 | Cite as

The Fundamental Group

  • Daniel Bump
Part of the Graduate Texts in Mathematics book series (GTM, volume 225)


In this chapter, we will look more closely at the fundamental group of a compact Lie group G. We will show that it is a finitely generated Abelian group and that every loop in G can be deformed into any given maximal torus. The key arguments are topological and are adapted from Adams [1].


Fundamental Group Maximal Torus Dense Open Subset Finite Union Local Homeomorphism 
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Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • Daniel Bump
    • 1
  1. 1.Department of MathematicsStanford UniversityStanfordUSA

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