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Categorical length, relative L-S category and higher Hopf invariants

100%

Iwase N.

Banach Center Publications

2009

tom 85

nr 1

205-224

In this paper we introduce the categorical length, a homotopy version of Fox categorical sequence, and an extended version of relative L-S category which contains the classical notions of Berstein-Ganea and Fadell-Husseini. We then show that, for a space or a pair, the categorical length for categorical sequences is precisely the L-S category or the relative L-S category in the sense of Fadell-Husseini respectively. Higher Hopf invariants, cup length, module weights, and recent computations by Kono and the author are also studied within this unified L-S theory based on the categorical length of categorical sequences.

On Lusternik-Schnirelmann category of SO(10)

63%

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 Banach Center Publications

1 Fundamenta Mathematicae

2 Iwase N.

1 Miyauchi T.

1 2016

1 2009

Wyniki wyszukiwania

Categorical length, relative L-S category and higher Hopf invariants

On Lusternik-Schnirelmann category of SO(10)