Work

Gyration stability for projective planes

Year: 2025

Type: article

Abstract: Gyrations are operations on manifolds that arise in geometric topology, where a manifold $M$ may exhibit distinct gyrations depending on the chosen twisting. For a given $M$, we ask a natural question: do all gyrations of $M$ share the same homotopy type regardless of the twisting? A manifold with this property is said to have gyration stability. Inspired by recent work by Duan, which demonstrated that the quaternionic projective plane is not gyration stable with respect to diffeomorphism, we explore this question for projective planes in general. We obtain a complete description of gyration stability for the complex, quaternionic, and octonionic projective planes up to homotopy.

Source: Topology and its Applications

DOI: 10.1016/j.topol.2025.109420

Authors: Sebastian Chenery, Stephen Theriault

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,920

Funders: Engineering and Physical Sciences Research Council, Heilbronn Institute for Mathematical Research

Award: DTP 2224 University of Southampton