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
Accepted

Knotted concordances of slice links

I think this is likely an unknown question. Namely, the negation of 3) would follow from 1) and 2) if strongly slice links are strongly ribbon (which seems to be open) ribbon disks bounding the ...
Ian Agol's user avatar
  • 66.9k
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
  • 43.1k
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
  • 18.6k
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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