Surfaces in 4-space
The low-dimensional topology sky is now richer for one more book treating surfaces in 4-space. The book treats the theory of knotting of surfaces in 4-space presenting up to date results and research that has been flourishing during the last decades. It is a joint work of three authors who are already experienced in writing books about this subject: see e.g. [\textit{J. S. Carter} and \textit{M. Saito}, Knotted surfaces and their diagrams, Math. Surveys and Monographs 55 (1998; Zbl 0904.57010); \textit{S. Kamada}, Braid and knot theory in dimension four, Math. Surveys and Monographs 95 (2002; Zbl 0993.57012)]. Let us scan the titles of the chapters to get an idea of the contents. The book is divided into four chapters entitled: 1. Diagrams of Knotted Surfaces 2. Constructions of Knotted Surfaces 3. Topological Invariants 4. Quandle Cocycle Invariants. An appendix brings the list of quandles of order 3, 4, 5, 6 and their homology groups. All maps in the book, and consequently the knots, are assumed to be smooth (of class \(C^\infty\)) or PL locally flat. Each notion is precisely defined with a short historical account included. The results are gradually introduced, illustrated by examples, and original references are always cited. The reader is advised if a result has a higher dimensional counterpart. The book contains an exhaustive list of references and the index. It represents a nice, useful and reliable encyclopaedic presentation of the above mentioned subject up to the date it was put in print.
scientific article; zbMATH DE number 2121101