TL;DR
This paper explores the relationship between twist and modification constructions in differential geometry, demonstrating how elementary deformations connect them and applying these ideas to classify hyperK"ahler manifolds.
Contribution
It introduces a link between twist and modification constructions via elementary deformations and applies this to classify hyperK"ahler four-manifolds with symmetries.
Findings
Elementary deformations connect twist and modification constructions.
Constructed hyperK"ahler and strong HKT structures using twists.
Classified complete hyperK"ahler four-manifolds with tri-Hamiltonian symmetry.
Abstract
The twist construction is a geometric T-duality that produces new manifolds from old, works well with for example hypercomplex structures and is easily inverted. It tends to destroy properties such as the hyperK\"ahler condition. On the other hand modifications preserve the hyperK\"ahler property, but do not have an obvious inversion. In this paper we show how elementary deformations provide a link between the two constructions, and use the twist construction to build hyperK\"ahler and strong HKT structures. In the process, we provide a full classification of complete hyperK\"ahler four-manifolds with tri-Hamiltonian symmetry and study a number singular phenomena in detail.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.