Poisson cohomology of broken Lefschetz fibrations |
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Affiliation: | 1. Department of Mathematics, Aristotle University of Thessaloniki, Thessaloniki 54124, Greece;2. Department of Mathematics, KU Leuven, Celestijnenlaan 200B, Leuven B-3001, Belgium |
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Abstract: | We compute the formal Poisson cohomology of a broken Lefschetz fibration by calculating it at fold and Lefschetz singularities. Near a fold singularity the computation reduces to that for a point singularity in 3 dimensions. For the Poisson cohomology around singular points we adapt techniques developed for the Sklyanin algebra. As a side result, we give compact formulas for the Poisson coboundary operator of an arbitrary Jacobian Poisson structure in 4 dimensions. |
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Keywords: | Broken Lefschetz fibrations Poisson cohomology Isolated singularities Graded vector fields |
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