Fundamental domains for properly discontinuous affine groups

Abstract

We construct a fundamental region for the action on the $2d+1$-dimensional affine space of some free, discrete, properly discontinuous groups of affine transformations preserving a quadratic form of signature $(d+1,d)$, where $d$ is any odd positive integer.

This is the version published in Geometriae Dedicata. It incorporates the corrections suggested by the reviewer. Most of these are minor, except for one: I replaced the term 'Lagrangian' (which, given the context, was not quite proper) by 'MTIS' (short for 'maximal totally isotropic subspace')

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