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A
homology theory for tropical cycles on integral affine
manifolds and a perfect pairing
Helge Ruddat |
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Geometry & Topology 25 (2021) 3079–3132
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Abstract |
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We introduce a cap product pairing for homology and cohomology of tropical cycles on integral affine manifolds with singularities. We show the pairing is perfect over in degree when the manifold has at worst symple singularities. By joint work with Siebert, the pairing computes period integrals and its perfectness implies the versality of canonical Calabi–Yau degenerations. We also give an intersection-theoretic application for Strominger–Yau–Zaslow fibrations. The treatment of the cap product and Poincaré–Lefschetz by simplicial methods for constructible sheaves might be of independent interest. |
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Keywords
tropical homology, torus fibration, SYZ, integrable system,
toric degeneration, mirror symmetry, versality, affine
structure, Picard-Lefschetz
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Mathematical Subject Classification 2010
Primary: 14J32
Secondary: 05E45, 14D06, 14T05, 32S60, 55U10
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References |
Publication
Received: 27 February 2020
Revised: 25 July 2020
Accepted: 8 September 2020
Published: 30 November 2021
Proposed: Mark Gross
Seconded: Richard P Thomas, Dan Abramovich
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Authors |
| Helge Ruddat | |
| Mathematisches Institut Johannes Gutenberg-Universität Mainz Mainz Germany |
Universität Hamburg Hamburg Germany |
