On Lusternik-Schnirelmann category of SO(10)

Norio Iwase, and Toshiyuki Miyauchi. "On Lusternik-Schnirelmann category of SO(10)." Fundamenta Mathematicae 234.3 (2016): 201-227. <http://eudml.org/doc/286653>.

@article{NorioIwase2016,
abstract = {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 $F_\{i\}F^\{\prime \}₁ ⊂ F_\{i+1\}$ 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.},
author = {Norio Iwase, Toshiyuki Miyauchi},
journal = {Fundamenta Mathematicae},
keywords = {Lusternik-Schnirelmann category; special orthogonal groups; Hopf invariant; principal bundle},
language = {eng},
number = {3},
pages = {201-227},
title = {On Lusternik-Schnirelmann category of SO(10)},
url = {http://eudml.org/doc/286653},
volume = {234},
year = {2016},
}

TY - JOUR
AU - Norio Iwase
AU - Toshiyuki Miyauchi
TI - On Lusternik-Schnirelmann category of SO(10)
JO - Fundamenta Mathematicae
PY - 2016
VL - 234
IS - 3
SP - 201
EP - 227
AB - 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 $F_{i}F^{\prime }₁ ⊂ F_{i+1}$ 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.
LA - eng
KW - Lusternik-Schnirelmann category; special orthogonal groups; Hopf invariant; principal bundle
UR - http://eudml.org/doc/286653
ER -