We study the space of square-integrable harmonic forms over ALF gravitational instantons of type A K−1 and of type D K . We first calculate its dimension making use of a result by Hausel, Hunsicker and Mazzeo which relates the Hodge cohomology of a gravitational instanton M to the singular cohomology of a particular compactification X M of M. We then exhibit an explicit basis, exact for A K−1 and approximate for D K , and interpret geometrically the relations between M, X M and their cohomologies.
Harmonic forms on ALF gravitational instantons
Franchetti G
2014-01-01
Abstract
We study the space of square-integrable harmonic forms over ALF gravitational instantons of type A K−1 and of type D K . We first calculate its dimension making use of a result by Hausel, Hunsicker and Mazzeo which relates the Hodge cohomology of a gravitational instanton M to the singular cohomology of a particular compactification X M of M. We then exhibit an explicit basis, exact for A K−1 and approximate for D K , and interpret geometrically the relations between M, X M and their cohomologies.File in questo prodotto:
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