A COMBINATORIAL INVARIANT FOR SPHERICAL CR STRUCTURES

作者：Falbel Elisha^*; Wang Qingxue

来源：Asian Journal of Mathematics, 2013, 17(3): 391-422.

• Bloch group
• cross-ratio
• spherical CR structure

We study a cross-ratio of four generic points of S-3 which comes from spherical CR geometry. We construct a homomorphism from a certain group generated by generic configurations of four points in S-3 to the pre-Bloch group P(C). If M is a 3-dimensional spherical CR manifold with a CR triangulation, by our homomorphism, we get a P(C)-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 the Whitehead link complement, we show its invariant is a torsion in B(k) and for a triangulation of the complement of the 5(2)-knot we show that the invariant is not trivial and not a torsion element.

• 出版日期2013-9
• 单位复旦大学