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On Lusternik-Schnirelmann category of SO(10)

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Iwase N., Miyauchi T.

Fundamenta Mathematicae

2016

tom 234

nr 3

201-227

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 $F_{i}F'₁ ⊂ F_{i+1}$ 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 yield cat(E) ≤ m + 1.

Ograniczanie wyników

1 Fundamenta Mathematicae

1 Iwase N.

1 Miyauchi T.

1 2016

Wyniki wyszukiwania

On Lusternik-Schnirelmann category of SO(10)