Triangles in the Heisenberg Group

Abstract

<p>In the Heisenberg Lie group with the Carnot-Caratheodory metric, we classify geodesic triangles up to isometry in terms of side-length and geodesic parameters. We obtain an angle deficit formula for Heisenberg triangles. We construct classical moduli spaces <em>T</em> and S₃\T for ordered and for unordered Heisenberg triangles respectively, computing homotopy type and manifold properties of the spaces, and producing a compactification of <em>T</em> up to similarity under the non-isotropic dilation.</p>