In Chapter 7 of John M. Lee's book on topological manifolds, we find the following text on composable paths and the multiplication of path classes, [itex] [f] [/itex] ... ...(adsbygoogle = window.adsbygoogle || []).push({});

Lee, writes the following:

In the above text, Lee defines composable paths and then defines path multiplication of path classes (not paths themselves) ...

Why does develop the theory of the fundamental group in terms of equivalence classes of paths (loops) ... why not just define a group in terms of composable paths ...?

Hope someone can clarify this matter ...

Peter

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# Multiplication of Path Classes and the Fundamental Group

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