A construction of $D_k$ asymptotically locally flat gravitational instantons from Atiyah-Hitchin and Taub-NUT geometries

Michael Singer (University College London)

19-May-2020, 15:30-16:30 (4 years ago)

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 )


Geometria em Lisboa (IST)

Series comments: To receive the series announcements, which include the
Zoom access password*, please register in
math.tecnico.ulisboa.pt/seminars/geolis/index.php?action=subscribe#subscribe
*the last announcement for a seminar is sent 2 hours before the seminar.

Geometria em Lisboa video channel: educast.fccn.pt/vod/channels/bu46oyq74

Organizers: Jose Mourao*, Rosa Sena Dias, Sílvia Anjos*
*contact for this listing

Export talk to