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Apr 25, 2012 at 22:02 comment added Jamin Sheriff Thanks Mark. Knots and Links had everything I needed, except of course for $k=2$. I'm studying a very specific class of embeddings; I'm hoping that $H$ exists for them even when $k=2$ but I guess won't get that for free.
Apr 25, 2012 at 20:25 vote accept Jamin Sheriff
Apr 22, 2012 at 9:55 answer added Ryan Budney timeline score: 3
Apr 22, 2012 at 6:32 comment added Mark Grant Perhaps take a look at D. Rolfsen, Knots and Links, in particular the intro to Chapter 2. I think such a continuous $H$ always exists for $k>2$, but there may not necessarily exist a smooth $H$.
Apr 22, 2012 at 6:24 history edited Jamin Sheriff CC BY-SA 3.0
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Apr 22, 2012 at 5:26 history asked Jamin Sheriff CC BY-SA 3.0