Classical topology and combinatorial group theory / John Stillwell

This is the second edition of this well-known book, which emphasizes geometrical intuition and the historical origins of ideas and concepts in topology and combinatorial group theory. Apart from corrections (but the notion of path-homotopy is still defined without fixing the endpoints), a new chapter on Turing machines, the unsolvability of the word and isomorphism problem for groups and the homeomorphism problem for manifolds has been added. Following a recent approach of Cohen and Aanderaa to the word problem, complete and relatively short proofs of these unsolvability results are given. Already in the first edition algorithmic questions in topology and combinatorial group theory were one of the main threads, so the new chapter nicely completes the book. Additional interest comes from the recent developments in the area, such as group actions on simplicial and R-trees, hyperbolic and automatic groups, surgery and hyperbolic 3-manifolds, for which the book may serve as a first approach. (MathSciNet)

Bibliogr. p. [307]-318. Index