Extra-twisted connected sum $G_2$-manifolds

15-Apr-2021, 12:00-13:00 (3 years ago)

Abstract: The twisted connected sum construction of Kovalev produces many examples of closed Riemannian $7$-manifolds with holonomy group $G_2$ (a special class of Ricci-flat manifolds), starting from complex algebraic geometry data like Fano $3$-folds. If the pieces admit automorphisms, then adding an extra twist to the construction yields examples with a wider variety of topological features. I will describe the constructions and outline how one can use them to produce example of e.g. closed $7$-manifolds with disconnected moduli space of holonomy $G_2$ metrics, or pairs of $G_2$-manifolds that homeomorphic but not diffeomorphic. This is joint work with Diarmuid Crowley and Sebastian Goette.

algebraic geometrycombinatorics

Audience: researchers in the topic

( slides | video )


Online Nottingham algebraic geometry seminar

Series comments: Online geometry seminar, typically held on Thursday. This seminar takes place online via Microsoft Teams on the Nottingham University "Algebraic Geometry" team.

For recordings of past talks, copies of the speaker's slides, or to be added to the Team, please visit the seminar homepage at: kasprzyk.work/seminars/ag.html

Organizers: Alexander Kasprzyk*, Johannes Hofscheier*, Erroxe Etxabarri Alberdi
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