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Published **March 20, 1998**
by Birkhauser .

Written in English

- Geometry,
- Groups & group theory,
- Topology,
- Group Theory,
- Graphic Methods,
- Theory Of Groups,
- Mathematics,
- Science/Mathematics,
- Combinatorics,
- Mathematics / General

**Edition Notes**

Contributions | Lino Di Martino (Editor), William Kantor (Editor), Guglielmo Lunardon (Editor), Antonio Pasini (Editor), Maria Clara Tamburini (Editor) |

The Physical Object | |
---|---|

Format | Hardcover |

Number of Pages | 261 |

ID Numbers | |

Open Library | OL9090421M |

ISBN 10 | 3764358815 |

ISBN 10 | 9783764358815 |

This book is devoted to the theory of geometries which are locally Euclidean, in the sense that in small regions they are identical to the geometry of the Euclidean plane or Euclidean 3-space. Starting from the simplest examples, we proceed to develop a Price: $ Crystallographic groups and geometries: discrete groups.- A typical example: the geometry of the rectangle.- Classification of all locally Cn or Dn geometries.- On the proof of Theorems 1 and Crystals and their molecules.- IV. Geometries on the torus, complex numbers and Lobachevsky geometry.- The basic method of study is the use of groups of motions, both discrete groups and the groups of motions of geometries. The book does not presuppose on the part of the reader any preliminary knowledge outside the limits of a school geometry course. On September , a conference on Groups and Geometries took place in lovely Siena, Italy. It brought together experts and interested mathematicians from numerous countries. The scientific program centered around invited exposi tory lectures; there also were shorter research announcements.

Geometries and groups. [V V Nikulin; I R Shafarevich] -- This is a quite exceptional book, a lively and approachable treatment of an important field of mathematics given in a masterly style. Assuming only a school background, the authors develop locally. On September , a conference on Groups and Geometries took place in lovely Siena, Italy. It brought together experts and interested mathematicians from numerous countries. The scientific program centered around invited exposi tory lectures; there also were shorter research announcements, including talks by younger researchers. Geometries and Groups (Universitext) eBook: Viacheslav V. Nikulin, Igor R. Shafarevich, M. Reid: : Kindle Store5/5(2). This book explores these connections between group theory and geometry, introducing some of the main ideas of transformation groups, algebraic topology, and geometric group theory. The first half of the book introduces basic notions of group theory and studies symmetry groups in various geometries, including Euclidean, projective, and hyperbolic.

Since the classification of finite simple groups was announced in the subject has continued to expand opening many new areas of research. This volume contains a collection of papers, both survey and research, arising from the Durham conference in which the excellent progress of the decade was surveyed and new goals considered. Euclidean and other geometries are distinguished by the transformations that preserve their essential properties. Using linear algebra and transformation groups, this book provides a readable exposition of how these classical geometries are both differentiated and connected. Following Cayley and Klein, the book builds on projective and inversive geometry to construct . The book deals with fundamental structural aspects of algebraic and simple groups, Coxeter groups and the related geometries and buildings. All contributing authors are very active researchers in the topics related to the theme of the : Springer India. This book is devoted to the theory of geometries which are locally Euclidean, in the sense that in small regions they are identical to the geometry of the Euclidean plane or Euclidean 3-space. Starting from the simplest examples, we proceed to develop a general theory of such geometries, based on their relation with discrete groups of motions of.

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