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On cat(X p ).

Rivadeneyra Perez, Juan Julian (1992)

International Journal of Mathematics and Mathematical Sciences

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 real flag manifolds with cup-length equal to its dimension

Marko Radovanović (2020)

Czechoslovak Mathematical Journal

We prove that for any positive integers n 1 , n 2 , ... , n k there exists a real flag manifold F ( 1 , ... , 1 , n 1 , n 2 , ... , n k ) with cup-length equal to its dimension. Additionally, we give a necessary condition that an arbitrary real flag manifold needs to satisfy in order to have cup-length equal to its dimension.

On the homological category of 3-manifolds.

José Carlos Gómez Larrañaga, Francisco Javier González Acuña (1991)

Revista Matemática de la Universidad Complutense de Madrid

Let M be a closed, connected, orientable 3-manifold. Denote by n(S1 x S2) the connected sum of n copies of S1 x S2. We prove that if the homological category of M is three then for some n ≥ 1, H*(M) is isomorphic (as a ring) to H*(n(S1 x S2)).

On two results of Singhof

Augustin-Liviu Mare (1997)

Commentationes Mathematicae Universitatis Carolinae

For a compact connected semisimple Lie group G we shall prove two results (both related with Singhof’s paper [13]) on the Lusternik-Schnirelmann category of the adjoint orbits of G , respectively the 1-dimensional relative category of a maximal torus T in G . The techniques will be classical, but we shall also apply some basic results concerning the so-called 𝒜 -category (cf. [14]).

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