The space of Schwarz-Klein triangles
Alexandre Eremenko, Andrei Gabrielov

TL;DR
This paper characterizes the space of spherical triangles, showing it as a smooth 3-manifold with a specific topological structure, and describes how angles and sides relate analytically within this space.
Contribution
It provides a detailed geometric and topological description of the space of spherical triangles, including its manifold structure and analytic embedding.
Findings
The space of spherical triangles is a smooth connected orientable 3-manifold.
It is homotopy equivalent to the 1-skeleton of a cubic partition of the first octant.
Angles and sides are real analytic functions on this manifold, embedding it into a6^6.
Abstract
We describe the space of spherical triangles (in the sense of Schwarz and Klein). It is a smooth connected orientable 3-manifold, homotopy equivalent to the 1-skeleton of the cubic partition of the closed first octant in . The angles and sides are real analytic functions on this manifold which embed it to .
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology
