Volume 12, issue 2 (2012)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Geometric interpretation of simplicial formulas for the Chern–Simons invariant

Julien Marché

Algebraic & Geometric Topology 12 (2012) 805–827
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, ) 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