An introduction to arithmetic groups

Details An introduction to arithmetic groups An introduction to arithmetic groups

2004-03-23

arxiv.org/abs/math/0403390v1

Mathematics

Group Theory

Talks at the Conference ``Frontiers in Number Theory, Physics and Geometry'', Les Houches, March 9-21, 2003

Scientific paper

Arithmetic groups are groups of matrices with integral entries. We shall first discuss their origin in number theory (Gauss, Minkowski) and their role in the "reduction theory of quadratic forms". Then we shall describe these groups by generators and relations. The next topic will be: are all subgroups of finite index given by congruence conditions? Finally, we shall discuss rigidity properties of arithmetic groups.

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