zbMATH — the first resource for mathematics

How surfaces intersect in space. An introduction to topology. 2nd ed. (English) Zbl 0855.57001
Series on Knots and Everything. 2. Singapore: World Scientific. xviii, 318 p. (1995).
This unusual topology book centers around generic intersecting surfaces and their branching and multiple point behaviour. As the author says in his preface, the book might be subtitled “Topology from Scott Carter’s viewpoint”. Accordingly, it has a very personal and human flavour. It addresses not only mathematicians and, therefore, fear-inspiring technical arguments are kept to a minimum. Instead, there is an enormous wealth of illustrations: more than 200 pages contain pictures, and many of them are very elaborate. For instance, pages 190-200 are wholly devoted to drawing the Cromwell-Marar surfaces which sit in 3-space with one triple point and six branch points; the section on “Moving surfaces in four dimensions” (i.e., on the higher-dimensional analogues of Reidemeister moves and on related “movie moves”) contains 21 full pages of pictures, while pp. 241-268 depict an eversion of the two-dimensional sphere.
This book is a definite enrichment to the literature in low-dimensional topology.

57-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to manifolds and cell complexes
57M99 General low-dimensional topology
57R45 Singularities of differentiable mappings in differential topology
57R42 Immersions in differential topology
57Q45 Knots and links in high dimensions (PL-topology) (MSC2010)