HUNSICKER, E., 2017. Extended Hodge theory for fibred cusp manifolds. Journal of Topology and Analysis, [in press]
For a particular class of pseudo manifolds, we show that the intersection cohomology
groups for any perversity may be naturally represented by extended weighted L2 harmonic
forms for a complete metric on the regular stratum with respect to some weight determined
by the perversity. Extended weighted L2 harmonic forms are harmonic forms that are almost
in the given weighted L2 space for the metric in question, but not quite. This result is akin to
the representation of absolute and relative cohomology groups for a manifold with boundary
by extended harmonic forms on the associated manifold with cylindrical ends. In analogy
with that setting, in the unweighted L2 case, the boundary values of the extended harmonic
forms de ne a Lagrangian splitting of the boundary space in the long exact sequence relating
upper and lower middle perversity intersection cohomology groups.
This paper is closed access until 10 February 2018.