Generalized orientations and the Bloch invariant

2006/07/20 by Michel Matthey, Matthey, Michel, Wolfgang Pitsch +3
Mathematics · #19E99 #55N20 #55P43 #57M27 (Primary) #57M50 (Secondary) #Algebraic Topology (math.AT) #FOS: Mathematics #K-Theory and Homology (math.KT) #math.AT #math.KT #msc:19E99 #msc:55N20 #msc:55P43 #msc:57M27 #msc:57M50

paper · pdf · doi:10.48550/arxiv.math/0607496

16 pages

arxiv created 2006/07/20 · arxiv updated 2009/12/01

Abstract

For compact hyperbolic 3-manifolds we lift the Bloch invariant defined by Neumann and Yang to an integral class in K₃(C) Applying the Borel and the Bloch regulators, one gets back the volume and the Chern-Simons invariant of the manifold. We also discuss the non-compact case, in which there appears a Z/2-ambiguity.

Related

• Bloch invariants of hyperbolic 3-manifolds
• Hyperbolic 3-manifolds, the Bloch group, and the work of Walter Neumann
• Extended Bloch group and the Chern-Simons class (Incomplete working version)
• Rationality of secondary classes
• The renormalization of volume and Chern-Simons invariant for hyperbolic 3-manifolds