Geometric interpretation of simplicial formulas for the Chern-Simons invariant

Details Geometric interpretation of simplicial formulas for the Chern-Simons invariant Geometric interpretation of simplicial formulas for the Chern-Simons invariant

2010-11-13

arxiv.org/abs/1011.3139v1

Mathematics

Geometric Topology

22 pages, 2 figures

Scientific paper

We give a direct interpretation of Neumann's combinatorial formula for the Chern-Simons invariant of a 3-manifold with a representation in PSL(2,C) whose restriction to the boundary takes values in upper triangular matrices. Our construction does not involve group homology or Bloch group but is based on the construction of an explicit flat connection for each tetrahedron of a simplicial decomposition of the manifold.

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