In this chapter we discuss an important topological method for dealing with the rigid action of a group G on a CW complex X. This “Borel construction” is presented in Sect. 6.1; once it is in place, the Rebuilding Lemma 6.1.4 shows us how to alter X, without altering its homotopy type, to have more desirable properties. The important special case where X is a tree is discussed in §6.2. The reader may find it helpful to read Sects. 6.1 and 6.2 in parallel.
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(2008). The Borel Construction and Bass-Serre Theory. In: Topological Methods in Group Theory. Graduate Texts in Mathematics, vol 243. Springer, New York, NY. https://doi.org/10.1007/978-0-387-74614-2_6
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DOI: https://doi.org/10.1007/978-0-387-74614-2_6
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