Work

Surgery descriptions of orientation-reversing periodic maps on closed orientable 3-manifolds

Year: 2026

Type: article

Abstract: We study surgery descriptions of orientation-reversing periodic diffeomorphisms of compact orientable 3-manifolds in terms of standard symmetries of model manifolds. We develop a method for reducing the singular set by equivariant Dehn surgery, eliminating singular points with orientation-preserving local symmetries and connecting surface components. For periodic diffeomorphisms with reduced singular sets, we prove that such surgery descriptions exist in $$S^3$$ S 3 whenever the singular set contains no surface or contains a separating surface. The remaining cases are addressed through generalized surgery descriptions on other model manifolds. Furthermore, we show that the surgery descriptions can be chosen so that every surgery coefficient is an integer or a half-integer.

Source: Monatshefte für Mathematik

DOI: 10.1007/s00605-026-02224-z

Author: Toru Ikeda

Institution: Kindai University

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funder: Japan Society for the Promotion of Science