A small generating set for the balanced superelliptic handlebody group
Genki Omori

TL;DR
This paper establishes minimal generating sets for the balanced superelliptic handlebody group and related groups, advancing understanding of their algebraic structure with explicit generators.
Contribution
It provides the first known minimal generating sets for the balanced superelliptic handlebody group and the liftable Hilden group, including proofs of minimality in several cases.
Findings
The balanced superelliptic mapping class group is generated by four elements.
The liftable Hilden group is generated by three elements.
These generating sets are minimal in most cases.
Abstract
The balanced superelliptic handlebody group is the normalizer of the transformation group of the balanced superelliptic covering space in the handlebody group of the total space. We prove that the balanced superelliptic mapping class group is generated by four elements. To prove this, we also proved that the liftable Hilden group is generated by three elements. This generating set for the liftable Hilden group is minimal except for some hyperelliptic cases and the generating set for the balanced superelliptic mapping class group above is also minimal for several cases.
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.
Taxonomy
TopicsAdvanced Algebra and Geometry · Geometric and Algebraic Topology · Geometry and complex manifolds
