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Original question asked here. It is problem 16(c), section 1.1 of Hatcher's Algebraic Topology.

I'm trying to figure out an explicit homotopy that breaks the the entanglement. I suppose the first step would be to write down the path A explicitly. Any ideas?

Tian He
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  • What makes you think such a homotopy exists? – Paul Sinclair Mar 31 '20 at 12:17
  • @Paul...The projection of A to $S^1$ and $D^2$ are both null-homotopic and path connected, so the fundamental group $\pi_1(A)=0$, so there should exist a homotopy between A and a point in A. – Tian He Mar 31 '20 at 13:48
  • Sure there is. And it's very easy to produce. But it "breaks the entanglement" by ignoring it and having no issue with passing the curve through itself. – Paul Sinclair Mar 31 '20 at 15:44

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