Generalized K\"ahler manifolds via mapping tori
Beatrice Brienza, Anna Fino
TL;DR
This paper constructs new examples of generalized K"ahler manifolds using mapping tori derived from products of 3-tori and compact K"ahler or hyperK"ahler manifolds, exploring their properties and recovering known cases.
Contribution
It introduces a novel method to generate generalized K"ahler manifolds via mapping tori, including non-K"ahler examples, and analyzes their cohomological properties.
Findings
Constructed new non-K"ahler generalized K"ahler manifolds.
Recovered known generalized K"ahler solvmanifolds.
Analyzed formality and Dolbeault cohomology of the examples.
Abstract
Starting from the product of a -torus and a compact K\"ahler (respectively, hyperK\"ahler) manifold we construct via mapping tori generalized K\"ahler manifolds of split (respectively, non-split) type. In this way we obtain new non-K\"ahler examples and we recover the known examples of generalized K\"ahler solvmanifolds. Moreover, we investigate the formality and the Dolbeault cohomology of the generalized K\"ahler mapping tori.
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Taxonomy
TopicsGeometry and complex manifolds · Algebraic Geometry and Number Theory · Homotopy and Cohomology in Algebraic Topology