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Mar 1, 2014 at 19:09 comment added Stefan Friedl In fact Ito proves the statement I claimed for genus one knots which are not trefoils. So no contradiction with what Ian is saying.
Feb 28, 2014 at 20:23 history edited Ian Agol CC BY-SA 3.0
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Feb 28, 2014 at 7:21 comment added Stefan Friedl thanks Ian! I was thinking about this because of the following paper by Ito front.math.ucdavis.edu/1307.5115 where (as far as I can see) he shows in the proof of Theorem 1, that a genus one knot can not have an immersed Seifert surface of genus one with a homologically non-trivial curve. This seems to fit nicely with your answer, you `need some space' to get such immersed Seifert surfaces.
Feb 28, 2014 at 7:21 vote accept Stefan Friedl
Feb 28, 2014 at 5:28 history answered Ian Agol CC BY-SA 3.0