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arXiv · 1910.01780

Bott-Chern homology, Bott-Chern differential cohomology and the Hodge conjecture

Jyh-Haur Teh·Chin-Jui Yang
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Abstract

We propose a version of the Hodge conjecture in Bott-Chern cohomology and using results from characterizing real holomorphic chains by real rectifiable currents to provide a proof for this question. We define a Bott-Chern differential cohomology and use atomic section theory of Harvey and Lawson to construct refined Bott-Chern classes for holomorphic vector bundles in this differential cohomology. These refined Bott-Chern classes transform naturally to standard Chern classes, Bott-Chern classes and Cheeger-Simons' refined Chern classes.

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Jyh-Haur Teh, Chin-Jui Yang. 2019-10-04. Bott-Chern homology, Bott-Chern differential cohomology and the Hodge conjecture. https://arxiv.org/abs/1910.01780

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