Groups and Geometry

This 1985 book is an introduction to certain central ideas in group theory and geometry.

Roger C. Lyndon (Author)

9780521316941, Cambridge University Press

Paperback, published 14 March 1985

230 pages
22.8 x 15.2 x 1.4 cm, 0.348 kg

This book, which was originally published in 1985 and has been translated and revised by the author from notes of a course, is an introduction to certain central ideas in group theory and geometry. Professor Lyndon emphasises and exploits the well-known connections between the two subjects and, whilst keeping the presentation at a level that assumes only a basic background in mathematics, leads the reader to the frontiers of current research at the time of publication. The treatment is concrete and combinatorial with a minimal use of analytic geometry. In the interest of the reader's intuition, most of the geometry considered is two-dimensional and there is an emphasis on examples, both in the text and in the problems at the end of each chapter.

1. Symmetries and groups
2. Isometries of the Euclidian Plane
3. Subgroups of the groups of isometries of the plane
4. Discontinuous groups of isometries of the Euclidean plane: plane crystallographic groups
5. Regular tesselations in higher dimensions
6. Incidence geometry of the affine plane
7. Projective geometry
8. Inversive geometry
9. Hyperbolic geometry
10. Fuscian groups
References
Index.

Subject Areas: Algebra [PBF]