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 ...

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 ...

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 ...

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-...

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 (...

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 ...

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