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9 votes

Is there a known invariant for knotted surfaces defined by skein relations?

It is known that a knotted surface can be presented by a marked graph diagram, which is just a knot diagram while some crossing points are equipped with markers. On the other hand, two marked graph ...
Zhiyun Cheng's user avatar
7 votes

topological "milnor's conjecture" on torus knots.

I realize the following answer comes somewhat belated. Rudolph worked on this (Some topologically locally-flat surfaces in the complex projective plane), and more recently Baader, Feller, Liechti and ...
Lukas Lewark's user avatar
6 votes

Is there a known invariant for knotted surfaces defined by skein relations?

The answer might depend a bit on exactly what you want; perhaps giving a precise formulation is the hard part! There was an important first step in this direction for the Alexander polynomial, by ...
Danny Ruberman's user avatar
5 votes

Is the Artin Spin construction related to the suspension functor?

Although this is not exactly an answer to your question, it answers a slightly different question in a strong affirmative. In my paper A family of embedding spaces, Geom. Topol. Monogr. 13 (2008) 41-...
Ryan Budney's user avatar
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5 votes
Accepted

Is the Artin Spin construction related to the suspension functor?

This question is answered in section 4 of my first paper (with Alex Suciu) Klein, John R.; Suciu, Alexander I. Inequivalent fibred knots whose homotopy Seifert pairings are isometric. Math. Ann. 289 (...
John Klein's user avatar
  • 18.5k
2 votes
Accepted

Isotopy extension theorem: how non-unique is ambient isotopy

If I interpret the question correctly then the answer is "yes". You seem to be asking whether, if $H'$ is an isotopy satisfying the same conditions as $H$, there must be a one-parameter family of such ...
Tom Goodwillie's user avatar

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