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Cohomologies of locally conformally symplectic manifolds and solvmanifolds

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arxiv 1703.05512 v2 pith:X6IZQUHM submitted 2017-03-16 math.DG math.SG

Daniele Angella , Alexandra Otiman , Nicoletta Tardini This is my paper · ORCID
classification math.DGmath.SG
keywords manifoldscohomologiesconditionconformallylocallyoeljeklaus-tomaparticularprecisely
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abstract

We study the Morse-Novikov cohomology and its almost-symplectic counterpart on manifolds admitting locally conformally symplectic structures. More precisely, we introduce lcs cohomologies and we study elliptic Hodge theory, dualities, Hard Lefschetz Condition. We consider solvmanifolds and Oeljeklaus-Toma manifolds. In particular, we prove that Oeljeklaus-Toma manifolds with precisely one complex place, and under an additional arithmetic condition, satisfy the Mostow property. This holds in particular for the Inoue surface of type $S^0$.

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  1. Boundary framings for locally conformally symplectic four-manifolds

    math.AT 2025-02 reject novelty 5.0 of 10

    The paper proposes a rational homotopy model for a classifying space of locally conformally symplectic four-manifolds and a cobordism category of three-manifolds with Omega^2 S^2-bundle framings, but the standalone te...

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