Abstract
We have mentioned the strong influence of geometry, topology, and parts of analysis on the origin and development of combinatorial group theory, as well as the application of geometric and topological methods to abstract group theory. Here we develop some of the most elementary of these methods, partly because of the intrinsic interest of these connections, partly to present geometric proofs of some theorems that are proved by other means elsewhere, and partly to provide a basis for the geometric ideas that enter into our discussion of small cancellation theory in Chapter V. We have tried to include in this chapter everything of a geometric nature appropriate to our topic and accessible by our limited means, except for the systematic development of small cancellation theory.
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© 2001 Springer-Verlag Berlin Heidelberg
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Lyndon, R.C., Schupp, P.E. (2001). Geometric Methods. In: Combinatorial Group Theory. Classics in Mathematics, vol 89. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-61896-3_3
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DOI: https://doi.org/10.1007/978-3-642-61896-3_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-41158-1
Online ISBN: 978-3-642-61896-3
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