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Intuitive combinatorial topology. Transl. from the Russian by Abe Shenitzer. With the editorial assistance of John Stillwell. (English) Zbl 0971.57002

Universitext. New York, NY: Springer. xii, 141 p. (2001).
The book is organized as follows. Chapter 1 – Topology of curves; Chapter 2 – Topology of surfaces; Chapter 3 – Homotopy and homology, and a supplementary chapter dealing with an interesting application of topology to the theory of nematic liquid crystals. The text is written in an enthusiastic and lively style. The proofs are given in detail, without prerequisites. In each part of the book, the reader will find numerous carefully illustrative examples. The book is well suited for advanced undergraduates or beginning graduates interested in finding out what topology is all about. The book offers 213 problems, gives 68 examples and is illustrated by over 210 figures.
For the review of the Russian original see Zbl 0606.57001.

MSC:

57-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to manifolds and cell complexes
55-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic topology
57N05 Topology of the Euclidean \(2\)-space, \(2\)-manifolds (MSC2010)
57R25 Vector fields, frame fields in differential topology
57M25 Knots and links in the \(3\)-sphere (MSC2010)
57M30 Wild embeddings
57M05 Fundamental group, presentations, free differential calculus
55N10 Singular homology and cohomology theory
55Q05 Homotopy groups, general; sets of homotopy classes
05C15 Coloring of graphs and hypergraphs
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