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Birkhäuser

Generalized Polygons

  • Book
  • © 1998

Overview

Authors:
  1. Hendrik Maldeghem

    1. Department of Pure Mathematics, University of Gent, Gent, Belgium

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Part of the book series: Monographs in Mathematics (MMA, volume 93)

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-xv
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  2. Basic Concepts and Results

    • Hendrik van Maldeghem
    Pages 1-47

  3. Classical Polygons

    • Hendrik van Maldeghem
    Pages 49-86

  4. Coordinatization and Further Examples

    • Hendrik van Maldeghem
    Pages 87-134

  5. Homomorphisms and Automorphism Groups

    • Hendrik van Maldeghem
    Pages 135-171

  6. The Moufang Condition

    • Hendrik van Maldeghem
    Pages 173-238

  7. Characterizations

    • Hendrik van Maldeghem
    Pages 239-303

  8. Ovoids, Spreads and Self-Dual Polygons

    • Hendrik van Maldeghem
    Pages 305-359

  9. Projectivities and Projective Embeddings

    • Hendrik van Maldeghem
    Pages 361-405

  10. Topological Polygons

    • Hendrik van Maldeghem
    Pages 407-425

  11. Back Matter

    Pages 427-504
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Keywords

About this book

This book is intended to be an introduction to the fascinating theory ofgeneralized polygons for both the graduate student and the specialized researcher in the field. It gathers together a lot of basic properties (some of which are usually referred to in research papers as belonging to folklore) and very recent and sometimes deep results. I have chosen a fairly strict geometrical approach, which requires some knowledge of basic projective geometry. Yet, it enables one to prove some typically group-theoretical results such as the determination of the automorphism groups of certain Moufang polygons. As such, some basic group-theoretical knowledge is required of the reader. The notion of a generalized polygon is a relatively recent one. But it is one of the most important concepts in incidence geometry. Generalized polygons are the building bricks of Tits buildings. They are the prototypes and precursors of more general geometries such as partial geometries, partial quadrangles, semi-partial ge­ ometries, near polygons, Moore geometries, etc. The main examples of generalized polygons are the natural geometries associated with groups of Lie type of relative rank 2. This is where group theory comes in and we come to the historical raison d'etre of generalized polygons. In 1959 Jacques Tits discovered the simple groups of type 3D by classifying the 4 trialities with at least one absolute point of a D -geometry. The method was 4 predominantly geometric, and so not surprisingly the corresponding geometries (the twisted triality hexagons) came into play. Generalized hexagons were born.

Reviews

"… If you believe that incidence geometry is out of date, this book will prove you wrong. If you are interested in geometry and want to get introduced to fascinating recent concepts, this book will be a good starting point and a trustworthy companion for most of your way. If you are already doing research in incidence geometry, this book will bring you up to date on generalized polygons and provide a very convincing notation. In addition, its bibliography and its almost complete collection of results on generalized polygons will make it an indispensable tool. If you are eager to do some research, the author offers ten open problems."

–Zentralblatt Math

Authors and Affiliations

  • Department of Pure Mathematics, University of Gent, Gent, Belgium

    Hendrik Maldeghem

Bibliographic Information

  • Book Title: Generalized Polygons

  • Authors: Hendrik Maldeghem

  • Series Title: Monographs in Mathematics

  • DOI: https://doi.org/10.1007/978-3-0348-8827-1

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Basel AG 1998

  • Hardcover ISBN: 978-3-7643-5864-8Due: 01 December 1998

  • Softcover ISBN: 978-3-0348-9789-1Published: 01 September 2014

  • eBook ISBN: 978-3-0348-8827-1Published: 09 November 2013

  • Series ISSN: 1017-0480

  • Series E-ISSN: 2296-4886

  • Edition Number: 1

  • Number of Pages: XV, 502

  • Number of Illustrations: 29 b/w illustrations

  • Topics: Algebraic Geometry

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