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Diffeology of the infinite Hopf fibration

Patrick Iglesias-Zemmour — 2007

Banach Center Publications

We introduce diffeological real or complex vector spaces. We define the fine diffeology on any vector space. We equip the vector space 𝓗 of square summable sequences with the fine diffeology. We show that the unit sphere 𝓢 of 𝓗, equipped with the subset diffeology, is an embedded diffeological submanifold modeled on 𝓗. We show that the projective space 𝓟, equipped with the quotient diffeology of 𝓢 by 𝓢¹, is also a diffeological manifold modeled on 𝓗. We define the Fubini-Study symplectic...

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