Geometric interpretation of simplicial formulas for the Chern–Simons invariant

Marché, Julien

doi:10.2140/agt.2012.12.805

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Geometric interpretation of simplicial formulas for the Chern–Simons invariant

Julien Marché

Algebraic & Geometric Topology 12 (2012) 805–827

DOI: 10.2140/agt.2012.12.805

Abstract

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.

Keywords

Chern–Simons, triangulation, simplicial formula

Mathematical Subject Classification 2010

Primary: 57M27, 58J28

References

Publication

Received: 24 January 2011

Revised: 27 January 2012

Accepted: 18 October 2011

Published: 17 April 2012

Authors

Julien Marché
Centre de Mathématiques Laurent Schwartz École Polytechnique Route de Saclay 91128 Palaiseau Cedex France

Volume 12, issue 2 (2012)