Abstract
So far, we have learned how to compute fundamental groups for a few spaces, such as the circle, the sphere, the torus, and the annulus. But there are many more spaces whose fundamental groups we would like to know. In order to work them out, we will try to build them up from spaces whose fundamental groups we already know. Before we introduce the general theorem, let us look at an example, that of the wedge of two circles, meaning two circles that intersect at exactly one point (see Figure 12.1).
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Notes
- 1.
By a “word,” we simply mean an element of the free group \(F_2\), which is a string of symbols a, b, \(a^{-1}\), and \(b^{-1}\). The trivial word is the string with no characters in it.
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Bray, C., Butscher, A., Rubinstein-Salzedo, S. (2021). The Seifert–Van Kampen Theorem. In: Algebraic Topology. Springer, Cham. https://doi.org/10.1007/978-3-030-70608-1_12
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DOI: https://doi.org/10.1007/978-3-030-70608-1_12
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