Classical Topology and Combinatorial Group Theory

This introduction to topology stresses its geometric and combinatorial aspects. By focusing on the historical background it also stresses the intuitive aspects and the visual interpretation of results. By limiting the attention to dimensions fewer than 3 the discussion remains close to concrete, physical experience while still providing ample scope for analytic geometric and algebraic ideas. By focusing on the fundamental group in the interaction with combinatorial group theory, the discussion is able not only to use the generality of the combinatorial approach but also to emphasize the two-way interaction between topology and algebra. The book includes algorithms for topological problems. While most of the results and proofs presented here are known, some have been simplified or placed in a new perspective. Over 300 illustrations, many interesting exercises, and challenging open problems are included.