Overview
- Contains theorems characterizing the classical projective spaces, polar spaces and geometries of exceptional Lie groups, which are combined with proofs in one source
- Contains an entirely new treatment of buildings
- Students can follow all the proofs from elementary first principles without any appeal to external publications
- Includes supplementary material: sn.pub/extras
Part of the book series: Universitext (UTX)
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Table of contents (18 chapters)
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The classical geometries.
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Applications to other Lie incidence geometries.
Reviews
From the reviews:
“In this expansive volume, Shult (Kansas State Univ.) attempts to provide a thorough, self-contained characterization of geometries of Lie type by means of local axioms on points and lines. … There is enough material here for several semester-long graduate courses; alternatively, the book could be used as a reference work. Shult makes every effort to remain chatty … and intuitive while ensuring precision and detail. Summing Up: Recommended. Graduate students and researchers.” (S. J. Colley, Choice, Vol. 48 (11), July, 2011)
“This book presents characterizations of the classical geometries of Lie type by axioms on points and lines; it is a teaching book with detailed proofs, written for beginning graduate students. … Most chapters end with a set of exercises … . The whole book shows the author’s love of incidence geometry and of teaching.” (Theo Grundhöfer, Mathematical Reviews, Issue 2011 m)
“Shult has designed the book as a self-contained resource for a graduate student who plans to pursue research in this area. … the book gives detailed proofs and offers exercises at the end of each chapter, organized by topic. … geometrically inclined readers will wish to illustrate the text, in addition to working through the official exercises. … the intensity of detail and sparsity of illustrations make it more suitable as a handbook for experts … .” (Ursula Whitcher, The Mathematical Association of America, July, 2012)
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Points and Lines
Book Subtitle: Characterizing the Classical Geometries
Authors: Ernest Shult
Series Title: Universitext
DOI: https://doi.org/10.1007/978-3-642-15627-4
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2011
Softcover ISBN: 978-3-642-15626-7Published: 20 December 2010
eBook ISBN: 978-3-642-15627-4Published: 13 December 2010
Series ISSN: 0172-5939
Series E-ISSN: 2191-6675
Edition Number: 1
Number of Pages: XXII, 676
Number of Illustrations: 88 b/w illustrations
Topics: Geometry, Topological Groups, Lie Groups