A combinatorial invariant for Spherical CR structures

الأصل · EN

We study a cross-ratio of four generic points of S³ which comes from spherical CR geometry. We construct a homomorphism from a certain group generated by generic configurations of four points in S³ to the pre-Bloch group P(). If M is a 3-dimensional spherical CR manifold with a CR triangulation, by our homomorphism, we get a P()-valued invariant for M. We show that when applying to it the Bloch-Wigner function, it is zero. Under some conditions on M, we show the invariant lies in the Bloch group B(k), where k is the field generated by the cross-ratio. For a CR triangulation of Whitehead link complement, we show its invariant is a non-trivial torsion in B(k).