Hyperbolic 3-manifolds, the Bloch group, and the work of Walter Neumann

2023/04/25 by Garoufalidis, Stavros, Zagier, Don
#FOS: Mathematics #FOS: Physical sciences #Geometric Topology (math.GT) #High Energy Physics - Theory (hep-th)

paper · doi:10.48550/arxiv.2304.12545

Abstract

This is an article about the work of Walter Neumann on hyperbolic geometry, ideal triangulations of 3-manifolds, the volume and Chern-Simons invariants of 3-manifolds and their elements of the the Bloch group. The article focuses on the relations of these classical invariants and the impact of Neumann's work to quantum topology and to mathematical physics.

Related

• An experimental investigation of Neumann's conjecture
• Generalized orientations and the Bloch invariant
• Hilbert's 3rd Problem and invariants of 3-manifolds
• Bloch invariants of hyperbolic 3-manifolds
• Extended Bloch group and the Chern-Simons class (Incomplete working version)