Gyration stability for projective planes
Gyration stability for projective planes
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.
homotopy groups of spheres, manifold topology, projective planes, Homotopy groups of spheres, Manifold topology, Projective planes
Theriault, Stephen
5e442ce4-8941-41b3-95f1-5e7562fdef80
Chenery, Sebastian
99f297e1-d179-4187-9ce2-2e8f86774fb3
12 May 2025
Theriault, Stephen
5e442ce4-8941-41b3-95f1-5e7562fdef80
Chenery, Sebastian
99f297e1-d179-4187-9ce2-2e8f86774fb3
Theriault, Stephen and Chenery, Sebastian
(2025)
Gyration stability for projective planes.
Topology and its Applications, 369, [109420].
(doi:10.1016/j.topol.2025.109420).
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.
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GyrationStability_final
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Accepted/In Press date: 3 May 2025
e-pub ahead of print date: 8 May 2025
Published date: 12 May 2025
Keywords:
homotopy groups of spheres, manifold topology, projective planes, Homotopy groups of spheres, Manifold topology, Projective planes
Identifiers
Local EPrints ID: 502072
URI: http://eprints.soton.ac.uk/id/eprint/502072
ISSN: 0166-8641
PURE UUID: 8093551c-4607-401f-a5b2-ea9672e78c4b
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Date deposited: 16 Jun 2025 16:36
Last modified: 04 Sep 2025 02:14
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Author:
Sebastian Chenery
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