Involutions Fixing $F^n cup {ext{Indecomposable}}$

Canadian mathematical bulletin

Pedro L. Q. Pergher¹ 

[1] Departamento de Matemática, Universidade Federal de São Carlos, Caixa Postal 676, São Carlos, SP 13565-905, Brazil

关键词: involution;    projective space bundle;    indecomposable manifold;    splitting principle;    Stiefel-Whitney class;    characteristic number;   

DOI  :  10.4153/CMB-2011-051-4

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

Let $M^m$ be an $m$-dimensional, closed and smooth manifold, equipped with a smooth involution $Tcolon M^m o M^m$ whose fixed point set has the form $F^n cup F^j$, where $F^n$ and $F^j$ are submanifolds with dimensions $n$ and $j$, $F^j$ is indecomposable and $ n >j$. Write $n-j=2^pq$, where $q ge 1$ is odd and $p geq 0$, and set $m(n-j) = 2n+p-q+1$ if $p leq q + 1$and $m(n-j)= 2n + 2^{p-q}$ if $p geq q$. In this paper we show that $m le m(n-j) + 2j+1$. Further, we show that this bound is emph{almost} best possible, by exhibiting examples $(M^{m(n-j) +2j},T)$ where the fixed point set of $T$ has the form $F^n cup F^j$ described above, for every $2 le j

【 授权许可】

Unknown