Abstract
AbstractThis article studies an analogue of the work of Beasley and Witten [BW] for the Chern–Simons partition function on a Seifert Manifold for U(1) gauge group. A key point is that our gauge group is not simply connected, whereas this is an essential assumption in Beasley and Witten’s [BW] work. We are still able to use Beasley and Witten’s results, however, to derive a definition of a U(1) Chern–Simons partition function. We then compare this result to a definition of the U(1) Chern–Simons partition function given by Mihaela Manoliu [M], and find that the two definitions agree up to some undetermined multiplicative constant. These results lead to a natural interpretation of the Ray-Singer analytic (Reidemeister) torsion as a symplectic volume form on the moduli space of flat U(1) connections over a Seifert three-manifold.KeywordsChern–Simons gauge theoryReidemeister-Ray-Singer torsionsymplectic volume formlocalization
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