Citation for a knot theory statement

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    Knot theory Theory
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Discussion Overview

The discussion revolves around finding a citation for a specific statement related to knot theory, particularly concerning the unknottedness of smooth k-spheres embedded in ##R^n## under certain conditions. The inquiry seeks to identify the original source of this statement.

Discussion Character

  • Exploratory, Technical explanation

Main Points Raised

  • One participant requests a citation for the statement regarding the unknottedness of smooth k-spheres.
  • Another participant suggests a paper that may be relevant to the inquiry.
  • One participant expresses a belief that knottedness of spheres is a codimension-2 phenomenon.
  • A later reply references the paper linked earlier, indicating that it supports the idea of knottedness being related to codimension.

Areas of Agreement / Disagreement

Participants have not reached a consensus on the citation or the interpretation of knottedness, as differing views on the nature of knottedness are presented.

Contextual Notes

The discussion does not clarify the specific definitions or assumptions regarding knottedness or the conditions under which the statement applies.

BillKet
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Hello! Where can I find the source for this statement (i.e. a citation for it, ideally the original one): "any smooth k-sphere embedded in ##R^n## with 2n − 3k − 3 > 0 is unknotted". Thank you!
 
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I thought knottedness ( of spheres) is a codimension-2 phenomenon.
 
Your impression is to some extent borne out by the second and third sentences of the paper by Zeeman, linked in post #2.
 
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