Gyration Stability for Projective Planes

Autor:	Chenery, Sebastian, Theriault, Stephen
Rok vydání:	2024
Předmět:	Mathematics - Algebraic Topology Mathematics - Geometric Topology Primary 57N65 Secondary 55P15 57P10
Druh dokumentu:	Working Paper
Popis:	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. Comment: 39 pages, comments welcome
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2412.13931 Zobrazit plný text záznamu View this record from Arxiv