An analytic construction of dihedral ALF gravitational instantons
1 hour 12 mins,
133.19 MB,
MP3
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| Description: |
Auvray, H (Université Paris-Sud)
Monday 27 July 2015, 11:30-12:30 |
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| Created: | 2015-07-31 17:07 |
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| Collection: | Metric and Analytic Aspects of Moduli Spaces |
| Publisher: | Isaac Newton Institute |
| Copyright: | Auvray, H |
| Language: | eng (English) |
| Distribution: |
World
(downloadable)
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| Explicit content: | No |
| Aspect Ratio: | 16:9 |
| Screencast: | No |
| Bumper: | UCS Default |
| Trailer: | UCS Default |
| Abstract: | Gravitational instantons are 4-dimensional complete non-compact hyperkähler manifolds with some curvature decay at infinity. The asymptotic geometry of these spaces plays an important role in a conjectural classification; for example, instantons of euclidean, i.e. quartic, large ball volume growth, are completely classified by Kronheimer, whereas the cubic regime, i.e. the {\it ALF (Asymptotically Locally Flat)} case, is not fully understood yet. More precisely, ALF instantons with {\it cyclic topology at infinity} are classified by Minerbe; by contrast, a classification in the {\it dihedral} case at infinity is still unknown. A wide, conjecturally exhaustive, range of dihedral ALF instantons were constructed by Cherkis-Kapustin, adopting the moduli space point of view, and studied explicitly by Cherkis-Hitchin. I shall explain in this talk another construction of such spaces, based on the resolution of a Monge-Ampère equation in ALF geometry. |
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