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- W2950355532 abstract "Let $G$ be a compact connected Lie group and $p : Eto Sigma A$ be a principal G-bundle with a characteristic map $alpha : Ato G$, where $A=Sigma A_{0}$ for some $A_{0}$. Let ${K_{i}{to} F_{i-1}{hookrightarrow} F_{i} ,|, 1{le} i {le} n,, F_{0}{=} {ast} ; F_{1}{=} Sigma{K_{1}} ; text{and}; F_{n}{simeq} G }$ be a cone-decomposition of $G$ of length $m$ and $F'_{1}=Sigma{K'_{1}} subset F_{1}$ with $K'_{1} subset K_{1}$ which satisfy $F_{i}F'_{1} subset F_{i+1}$ up to homotopy for any $i$. Our main result is as follows: we have $operatorname{cat}(X) le m{+}1$, if firstly the characteristic map $alpha$ is compressible into $F'_{1}$, secondly the Berstein-Hilton Hopf invariant $H_{1}(alpha)$ vanishes in $[A, Omega F'_1{ast}Omega F'_1]$ and thirdly $K_{m}$ is a sphere. We apply this to the principal bundle $mathrm{SO}(9)hookrightarrowmathrm{SO}(10)to S^{9}$ to determine L-S category of $mathrm{SO}(10)$." @default.
- W2950355532 created "2019-06-27" @default.
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- W2950355532 date "2007-12-21" @default.
- W2950355532 modified "2023-09-26" @default.
- W2950355532 title "On Lusternik-Schnirelmann category of SO(10)" @default.
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