22109
20180228131630.0
0550-3213
10.1016/j.nuclphysb.2017.10.021
DOI
2017-10-31T21:22:55Z
Guadagnini, Enore
ORCID:0000-0001-6726-5466
Dipartimento di Fisica “E. Fermi” dell'Università di Pisa, Italy
INFN Sezione di Pisa, Largo B. Pontecorvo 2, Pisa, 56127, Italy
enore.guadagnini@unipi.it
Italy
Flat connections in three-manifolds and classical Chern–Simons invariant
2017-11-13
Elsevier
A 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.
Elsevier
CC-BY-3.0
http://creativecommons.org/licenses/by/3.0/
The Author(s)
2017-10-30
Mathieu, Philippe
ORCID:0000-0002-9498-7461
LAPTh, Université de Savoie, CNRS, Chemin de Bellevue, BP 110, Annecy-le-Vieux Cedex, F-74941, France
France
Thuillier, Frank
LAPTh, Université de Savoie, CNRS, Chemin de Bellevue, BP 110, Annecy-le-Vieux Cedex, F-74941, France
France
Nuclear Physics B
2017
382193
http://repo.scoap3.org/record/22109/files/main.xml
452993
http://repo.scoap3.org/record/22109/files/main.pdf
776703
http://repo.scoap3.org/record/22109/files/main.pdf?subformat=pdfa
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