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Jan 19, 2021 at 17:16 history edited Danny Ruberman CC BY-SA 4.0
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Jan 19, 2021 at 17:14 comment added Danny Ruberman Sorry, didn't read carefully! I was preparing an answer to your actual question but others beat me to it. I would prove it inductively, using the splitting along (n-1)--spheres.
Jan 19, 2021 at 14:50 comment added iou Right, but I'm interested in an unlinked and an unknotted case (as stated at the end of my question), in which, I think, my suggestion should be correct. But I do not see how I can prove that they are homotopy equivalent..
Jan 19, 2021 at 14:44 history answered Danny Ruberman CC BY-SA 4.0