Period domains for gravitational instantons


Tsung-Ju Lee (Harvard University, USA)
2023-05-23  09:30 - 11:00
Room 202, Astronomy and Mathematics Building

Gravitational instantons (GIs) are defined as non-compact, complete hyperkahler 4-manifolds with L^2 curvature tensors. By a recent result of Sun and Zhang, there are six types GIs in total: ALE, ALF, ALG, ALG*, ALH and ALH*. It is also known that there are only finitely many diffeomorphism types within each type. Recall that the set of possible cohomology classes supporting the hyperkahler triples of GIs within a fixed diffeomorphic type is called the period domain and one is able to define the period map in this context. The period domains for ALE, ALF and ALH are studied by Kronheimer, Chen--Chen, and Hein. 

Together with Y.-S. Lin, we characterized the period domains for ALG, ALG* and ALH* GIs by showing that the period maps are surjective in those cases. In this talk, I will explain our results and ideas in more detail. This is a joint work with Y.-S. Lin.