000022109 001__ 22109
000022109 005__ 20180228131630.0
000022109 022__ $$a0550-3213
000022109 0247_ $$2DOI$$a10.1016/j.nuclphysb.2017.10.021$$t2017-10-31T21:22:55Z
000022109 100__ $$aGuadagnini, Enore$$jORCID:0000-0001-6726-5466$$menore.guadagnini@unipi.it$$vINFN Sezione di Pisa, Largo B. Pontecorvo 2, Pisa, 56127, Italy$$vDipartimento di Fisica “E. Fermi” dell'Università di Pisa, Italy$$wItaly
000022109 245__ $$aFlat connections in three-manifolds and classical Chern–Simons invariant
000022109 260__ $$bElsevier$$c2017-11-13
000022109 520__ $$9Elsevier$$aA general method for the construction of smooth flat connections on 3-manifolds is introduced. The procedure is strictly connected with the deduction of the fundamental group of a manifold M by means of a Heegaard splitting presentation of M . For any given matrix representation of the fundamental group of M , a corresponding flat connection A on M is specified. It is shown that the associated classical Chern–Simons invariant assumes then a canonical form which is given by the sum of two contributions: the first term is determined by the intersections of the curves in the Heegaard diagram, and the second term is the volume of a region in the representation group which is determined by the representation of π1(M) and by the Heegaard gluing homeomorphism. Examples of flat connections in topologically nontrivial manifolds are presented and the computations of the associated classical Chern–Simons invariants are illustrated.
000022109 540__ $$aCC-BY-3.0$$uhttp://creativecommons.org/licenses/by/3.0/
000022109 542__ $$fThe Author(s)
000022109 592__ $$a2017-10-30
000022109 700__ $$aMathieu, Philippe$$jORCID:0000-0002-9498-7461$$vLAPTh, Université de Savoie, CNRS, Chemin de Bellevue, BP 110, Annecy-le-Vieux Cedex, F-74941, France$$wFrance
000022109 700__ $$aThuillier, Frank$$vLAPTh, Université de Savoie, CNRS, Chemin de Bellevue, BP 110, Annecy-le-Vieux Cedex, F-74941, France$$wFrance
000022109 773__ $$pNuclear Physics B$$y2017
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