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Distribution of Chern–Simons invariants

Abstract : Let M be a 3-manifold with a finite set X(M) of conjugacy classes of representations ρ : π1(M) → SU2. We study here the distribution of the values of the Chern-Simons function CS : X(M) → R/2πZ. We observe in some examples that it resembles the distribution of qua-dratic residues. In particular for specific sequences of 3-manifolds, the invariants tends to become equidistributed on the circle with white noise fluctuations of order |X(M)| −1/2. We prove that for a manifold with toric boundary the Chern-Simons invariants of the Dehn fillings M p/q have the same behaviour when p and q go to infinity and compute fluctuations at first order.
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Submitted on : Wednesday, July 3, 2019 - 11:56:28 AM
Last modification on : Tuesday, January 4, 2022 - 6:20:59 AM


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Julien Marche. Distribution of Chern–Simons invariants. Annales de l'Institut Fourier, Association des Annales de l'Institut Fourier, 2019, 69 (2), pp.753-762. ⟨10.5802/aif.3256⟩. ⟨hal-02171919⟩



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