Reciprocity of the Chern-Simons invariants of 3-manifolds

TL;DR

This paper explores reciprocity conjectures related to the Chern-Simons invariants of 3-manifolds, providing evidence and conditions under which these conjectures hold, especially involving Galois descent of K_3 groups.

Contribution

It introduces reciprocity conjectures for Chern-Simons invariants and demonstrates their validity under Galois descent conditions for K_3 groups.

Findings

Conjectures hold if Galois descent of K_3 groups is satisfied.

Provides supporting evidence for the reciprocity conjectures.

Links Chern-Simons invariants with algebraic K-theory.

Abstract

We pose reciprocity conjectures of the Chern-Simons invariants of 3-manifolds, and discuss some supporting evidence on the conjectures. Especially, we show that the conjectures hold if a Galois descent of a $K_3$-group is satisfied.