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 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 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm678-11-2015,
author = {Norio Iwase and Toshiyuki Miyauchi},
title = {On Lusternik-Schnirelmann category of SO(10)},
journal = {Fundamenta Mathematicae},
volume = {233},
year = {2016},
pages = {201-227},
zbl = {06602790},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm678-11-2015}
}
Norio Iwase; Toshiyuki Miyauchi. On Lusternik-Schnirelmann category of SO(10). Fundamenta Mathematicae, Tome 233 (2016) pp. 201-227. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm678-11-2015/