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arXiv · 1812.03730

$A_\mathfrak{q}$-components of geometric classes in compact Hermitian locally symmetric spaces

Arghya Mondal
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Abstract

Let $Γ\backslash G/K$ be a compact Hermitian locally symmetric space, where $G$ is simple. We study the components of a de Rham cohomology class of $Γ\backslash G/K$, with respect to the Matsushima decomposition, where the class is obtained by taking Poincaré dual of a totally geodesic complex analytic submanifold. Using an extension of the vanishing result of Kobayashi and Oda, we specify the existence of certain components of such cohomology classes when $G=\text{SU}(p,q), 5\le p\le q$.

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BibTeXRIS

Arghya Mondal. 2018-12-10. $A_\mathfrak{q}$-components of geometric classes in compact Hermitian locally symmetric spaces. https://arxiv.org/abs/1812.03730

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