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arXiv · 1006.2784

Some mixed Hodge structure on l^2-cohomology of covering of Kähler manifolds

Pascal Dingoyan
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Abstract

We give methods to compute l^2-cohomology groups of a covering manifolds obtained by removing pullback of a (normal crossing) divisor to a covering of a compact Kähler manifold. We prove that in suitable quotient categories, these groups admit natural mixed Hodge structure whose graded pieces are given by expected Gysin maps.

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Pascal Dingoyan. 2013-01-23. Some mixed Hodge structure on l^2-cohomology of covering of Kähler manifolds. https://doi.org/10.1007/s00208-013-0909-2

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