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On a smoothly stratified space, we identify intersection cohomology of anygiven perversity with an associated weighted $L^2$ cohomology for iteratedfibred cusp metrics on the smooth stratum. In particular given a Witt space, weidentify the $L^2$ cohomology of iterated fibred cusp metrics with the middleperversity intersection cohomology of the corresponding stratified space.

Hodge cohomology of iterated fibred cusp metrics on Witt spaces