Abstract: We study the space of square-integrable harmonic forms over ALF gravitational instantons of type AK−1 and of type DK. 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 XM of M. We then exhibit an explicit basis, exact for AK−1 and approximate for DK, and interpret geometrically the relations between M, XM and their cohomologies.
- Differential and Algebraic Geometry
- Solitons Monopoles and Instantons
ASJC Scopus subject areas
- Nuclear and High Energy Physics