Universal Poincar? duality for the intersection homology of branched and partial coverings of a pseudomanifold

Abstract

The work of Friedman and McClure shows that intersection homology satisfies a version of universal Poincar? duality for orientable pseudomanifolds. We extend their results to include regular covers defined solely over the regular strata. Our approach allows us to also prove a universal duality result for possibly non-orientable pseudomanifolds. We also show that for a special class of coefficient systems, which includes fields twisted by the orientation character, there is a non-universal Poincar? duality via cap products for intersection homology with twisted coefficients.--Abstract.