Some mixed Hodge structure on l2-cohomology of covering of K\"ahler manifolds
Abstract
We give methods to compute l2-cohomology groups of a covering manifolds obtained by removing pullback of a (normal crossing) divisor to a covering of a compact K\"ahler 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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