Monographs in Mathematics

Generalized Polygons

Authors: Maldeghem, Hendrik,van

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  • ISBN 978-3-0348-8827-1
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Softcover 103,99 €
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  • ISBN 978-3-0348-9789-1
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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"… If you believe that incidence geometry is out of date, this book will prove you wrong.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


Table of contents (9 chapters)

Table of contents (9 chapters)

Buy this book

eBook 85,59 €
price for Spain (gross)
  • ISBN 978-3-0348-8827-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 103,99 €
price for Spain (gross)
  • ISBN 978-3-0348-9789-1
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Generalized Polygons
Authors
Series Title
Monographs in Mathematics
Series Volume
93
Copyright
1998
Publisher
Birkhäuser Basel
Copyright Holder
Springer Basel AG
eBook ISBN
978-3-0348-8827-1
DOI
10.1007/978-3-0348-8827-1
Softcover ISBN
978-3-0348-9789-1
Series ISSN
1017-0480
Edition Number
1
Number of Pages
XV, 502
Number of Illustrations
29 b/w illustrations
Topics