# The noncanonical gluings of affine spaces

## Abstract

Given two geometries each equipped with a suitable parallelism giving
rise to the same geometry at infinity, a new geometry can be constructed
by gluing the two geometries together along their geometry at infinity.
If this identification is done by a non semilinear automorphism the gluing is called non canonical. In this paper we determine the noncanonical gluings of
affine spaces together with their universal coverings. We also construct the universal covering of the canonical gluings.

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