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On Lusternik-Schnirelmann category of SO(10)

Norio Iwase, Toshiyuki Miyauchi (2016)

Fundamenta Mathematicae

Let G be a compact connected Lie group and p: E → ΣA be a principal G-bundle with a characteristic map α: A → G, where A = ΣA₀ for some A₀. Let K i F i - 1 F i | 1 i m with F₀ = ∗, F₁ = ΣK₁ and Fₘ ≃ G be a cone-decomposition of G of length m and F’₁ = ΣK’₁ ⊂ F₁ with K’₁ ⊂ K₁ which satisfy F i F ' F i + 1 up to homotopy for all i. Then cat(E) ≤ m + 1, under suitable conditions, which is used to determine cat(SO(10)). A similar result was obtained by Kono and the first author (2007) to determine cat(Spin(9)), but that result could not...

On the space of maps inducing isomorphic connections

T. R. Ramadas (1982)

Annales de l'institut Fourier

Let ω be the universal connection on the bundle E U ( n ) B U ( n ) . Given a principal U ( n ) -bundle P M with connection A , we determine the homotopy type of the space of maps ϕ of M into B U ( n ) such that ( ϕ + E U ( n ) , ϕ + ω ) is isomorphic to ( P , A ) . Here ϕ + denotes pull-back.

On the uniform perfectness of groups of bundle homeomorphisms

Tomasz Rybicki (2019)

Archivum Mathematicum

Groups of homeomorphisms related to locally trivial bundles are studied. It is shown that these groups are perfect. Moreover if the homeomorphism isotopy group of the base is bounded then the bundle homeomorphism group of the total space is uniformly perfect.

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