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, Guido
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.
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