A construction of $D_k$ asymptotically locally flat gravitational instantons from Atiyah-Hitchin and Taub-NUT geometries
Michael Singer (University College London)
Abstract: Complete hyperKaehler 4-manifolds with cubic volume growth (and suitable decay of the curvature), also known as ALF gravitational instantons, are known to come in two families, according to the `fundamental group at infinity’. This group must be a finite subgroup of $SU(2)$ and the only possibilities compatible with cubic volume growth are the cyclic groups ($A_k$) and binary dihedral groups ($D_k$).
This talk will be about the construction of $D_k$ ALF gravitational instantons by a gluing construction in which the ingredients are the moduli space of centred charge-2 monopoles ($D_0$) and a particularly symmetric, but singular, $A_k$ ALF gravitational instanton. This construction was suggested in a paper of Sen (1997). It is also closely related to a construction due to Foscolo, in which hyperKaehler metrics are constructed on the $K3$ manifold that are `nearly’ collapsed to a 3-dimensional space.
This is joint work with Bernd Schroers.
algebraic geometrydifferential geometrysymplectic geometry
Audience: researchers in the topic
( video )
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