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In a remarkabale booklet `The sensual(quadratic) form', J.H. Conway introduces an elegant approach to integral binary quadratic forms. The main tool is a 3 valence tree which is in fact an SL_2(Z)-equivariant retract of the 2-dimensional hyperbolic space. Let A be the ring of integers of a quadratic imaginary extension of the field of rational numbers. The 3-dimensional hyperbolic space has a 2-dimensional, GL_2(A)-invariant retract. The retract is a CAT(0) complex. In this lecture I will explain how the retract can be used to derive some results on hermitian binary forms over the ring A. This is a joint work with Mladen Bestvina.
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