Harmonic forms on ALF gravitational instantons

Guido Franchetti

doi:10.1007/JHEP12(2014)075

Harmonic forms on ALF gravitational instantons

Guido Franchetti^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	1-14
Number of pages	14
Journal	Journal of High Energy Physics
Volume	2014
Issue number	12
DOIs	https://doi.org/10.1007/JHEP12(2014)075
Publication status	Published - 1 Jan 2014

Keywords

Differential and Algebraic Geometry
Solitons Monopoles and Instantons

ASJC Scopus subject areas

Nuclear and High Energy Physics

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10.1007/JHEP12(2014)075

Cite this

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abstract = "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.",

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N2 - 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.

AB - 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.

KW - Differential and Algebraic Geometry

KW - Solitons Monopoles and Instantons

U2 - 10.1007/JHEP12(2014)075

DO - 10.1007/JHEP12(2014)075

M3 - Article

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VL - 2014

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EP - 14

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

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ER -

Harmonic forms on ALF gravitational instantons

Abstract

Keywords

ASJC Scopus subject areas

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