Open Math Notes

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Welcome to AMS Open Math Notes, a repository of freely downloadable mathematical works in progress hosted by the American Mathematical Society as a service to researchers, teachers and students. These draft works include course notes, textbooks, and research expositions in progress. They have not been published elsewhere, and, as works in progress, are subject to significant revision. Visitors are encouraged to download and use these materials as teaching and research aids, and to send constructive comments and suggestions to the authors.

Open Math Notes Advisory Board:

  • Karen Vogtmann, Chair | University of Warwick
  • Mary Pugh | University of Toronto
  • Andrew Hwang | College of the Holy Cross
  • Robert Lazarsfeld | Stony Brook University


These are the notes of a two-hour one-semester course on CAT(0) cube complexes which I taught in Muenster during winter term 2012/2013. Topics covered are for example: Basic CAT(0) geometry, Gromov's link condition, half-space systems and Sageev's cubulation method, cubulating Coxeter groups and the Tits alternative. Since most of the students neither had a strong background in metric geometry nor in group theory I tried to keep the material as elementary and selfcontained as possible.

Petra Schwer
Otto von Guericke University

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