On Lusternik-Schnirelmann category of SO(10)

• Autorzy: Norio Iwase , Toshiyuki Miyauchi
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 57T15: Homology and cohomology of homogeneous spaces of Lie groups
• 55R10: Fiber bundles
• 55Q25: Hopf invariants
• 55M30: Ljusternik-Schnirelman (Lyusternik-Shnirel\cprime man) category of a space
• 57T10: Homology and cohomology of Lie groups

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2016
• Tom: 234
• Numer: 3
• Strony: 201-227

Daty

wydano

2016

Twórcy

autor

Norio Iwase

• Faculty of Mathematics, Kyushu University, Motooka 744, Fukuoka 819-0395, Japan

autor

Toshiyuki Miyauchi

• Department of Applied Mathematics, Faculty of Science, Fukuoka University, Fukuoka 814-0180, Japan

Identyfikatory

DOI

10.4064/fm678-11-2015