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Geometric and Topological Aspects of Coxeter Groups and Buildings
Zurich Lectures in Advanced Mathematics

Anne Thomas (The University of Sydney, Australia)

Geometric and Topological Aspects of Coxeter Groups and Buildings

ISBN print 978-3-03719-189-7, ISBN online 978-3-03719-689-2
DOI 10.4171/189
May 2018, 160 pages, softcover, 17 x 24 cm.
34.00 Euro

Coxeter groups are groups generated by reflections, and they appear throughout mathematics. Tits developed the general theory of Coxeter groups in order to develop the theory of buildings. Buildings have interrelated algebraic, combinatorial and geometric structures, and are powerful tools for understanding the groups which act on them.

These notes focus on the geometry and topology of Coxeter groups and buildings, especially nonspherical cases. The emphasis is on geometric intuition, and there are many examples and illustrations. Part I describes Coxeter groups and their geometric realisations, particularly the Davis complex, and Part II gives a concise introduction to buildings.

This book will be suitable for mathematics graduate students and researchers in geometric group theory, as well as algebra and combinatorics. The assumed background is basic group theory, including group actions, and basic algebraic topology, together with some knowledge of Riemannian geometry.

Keywords: Coxeter groups, buildings, Davis complexes