On cobrackets on the Wilson loops associated with flat GL(1, R)-bundles over surfaces
2018 年 41 巻 3 号 p. 591-619
詳細
2018 年 41 巻 3 号 p. 591-619
Let S be a closed connected oriented surface of genus g > 0. We study a Poisson subalgebra W1(g) of C∞(Hom(π1(S), GL(1, R))/GL(1, R)), the smooth functions on the moduli space of flat GL(1, R)-bundles over S. There is a surjective Lie algebra homomorphism from the Goldman Lie algebra onto W1(g). We classify all cobrackets on W1(g) up to coboundary, that is, we compute H1(W1(g), W1(g) ∧ W1(g)) ≅ Hom(Z2g, R). As a result, there is no cohomology class corresponding to the Turaev cobracket on W1(g).
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