A finite presentation for the balanced superelliptic handlebody group
Genki Omori, Yuya Yoshida
TL;DR
This paper provides a finite algebraic presentation for the balanced superelliptic handlebody group by constructing a finite presentation for the liftable Hilden group, advancing understanding of these complex topological groups.
Contribution
It introduces the first finite presentation for the balanced superelliptic handlebody group, utilizing a new presentation for the liftable Hilden group.
Findings
Finite presentation for the balanced superelliptic handlebody group
Finite presentation for the liftable Hilden group
Enhanced understanding of the group's algebraic structure
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 give a finite presentation for the balanced superelliptic handlebody group. To give this presentation, we construct a finite presentation for the liftable Hilden group.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Advanced Algebra and Geometry