論文

査読有り
2007年

High-codimensional knots spun about manifolds

ALGEBRAIC AND GEOMETRIC TOPOLOGY
  • Dennis Roseman
  • ,
  • Masamichi Takase

7
開始ページ
359
終了ページ
377
記述言語
英語
掲載種別
研究論文(学術雑誌)
DOI
10.2140/agt.2007.7.359
出版者・発行元
GEOMETRY & TOPOLOGY PUBLICATIONS

Using spinning we analyze in a geometric way Haefliger's smoothlyknotted (4k-1)-spheres in the 6k-sphere. Consider the 2-torus standardly embedded in the 3-sphere, which is further standardly embedded in the 6-sphere. At each point of the 2-torus we have the normal disk pair: a 4-dimensional disk and a 1-dimensional proper sub-disk. We consider an isotopy (deformation) of the normal 1-disk inside the normal 4-disk, by using a map from the 2-torus to the space of long knots in 4-space, first considered by Budney. We use this isotopy in a construction called spinning about a submanifold introduced by the first-named author. Our main observation is that the resultant spun knot provides a generator of the Haefliger knot group of knotted 3-spheres in the 6-sphere. Our argument uses an explicit construction of a Seifert surface for the spun knot and works also for higher-dimensional Haefliger knots.

Web of Science ® 被引用回数 : 2

リンク情報
DOI
https://doi.org/10.2140/agt.2007.7.359
Web of Science
https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=JSTA_CEL&SrcApp=J_Gate_JST&DestLinkType=FullRecord&KeyUT=WOS:000253946800017&DestApp=WOS_CPL

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