全部 标题 作者
关键词 摘要

OALib Journal期刊
ISSN: 2333-9721
费用:99美元

查看量下载量

相关文章

更多...
Mathematics  2009 

Spin structures and codimension-two homeomorphism extensions

Full-Text   Cite this paper   Add to My Lib

Abstract:

Let $\imath: M\to \RR^{p+2}$ be a smooth embedding from a connected, oriented, closed $p$-dimesional smooth manifold to $\RR^{p+2}$, then there is a spin structure $\imath^\sharp(\varsigma^{p+2})$ on $M$ canonically induced from the embedding. If an orientation-preserving diffeomorphism $\tau$ of $M$ extends over $\imath$ as an orientation-preserving topological homeomorphism of $\RR^{p+2}$, then $\tau$ preserves the induced spin structure. Let $\esg_\cat(\imath)$ be the subgroup of the $\cat$-mapping class group $\mcg_\cat(M)$ consisting of elements whose representatives extend over $\RR^{p+2}$ as orientation-preserving $\cat$-homeomorphisms, where $\cat=\topo$, $\pl$ or $\diff$. The invariance of $\imath^\sharp(\varsigma^{p+2})$ gives nontrivial lower bounds to $[\mcg_\cat(M):\esg_\cat(\imath)]$ in various special cases. We apply this to embedded surfaces in $\RR^4$ and embedded $p$-dimensional tori in $\RR^{p+2}$. In particular, in these cases the index lower bounds for $\esg_\topo(\imath)$ are achieved for unknotted embeddings.

Full-Text

Contact Us

service@oalib.com

QQ:3279437679

WhatsApp +8615387084133