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Oct 15, 2012 at 16:28 comment added Ryan Budney What I mean to say is that statement in the paper is fine, and that's a fairly standard level of detail for that area.
Oct 15, 2012 at 16:28 comment added Ryan Budney There are some situations of reasonable generality where what you ask for is true, but as stated in your first paragraph, it's false. For example, if $X$ is a 3-ball, $V$ and $N$ an embedded interval or a point respectively. The complements do not have to be homotopy-equivalent. Your latter comment about the paper, though, that's fine. It's part of the tubular neighbourhood theorem.
Oct 15, 2012 at 16:26 history edited palio CC BY-SA 3.0
deleted 116 characters in body; added 2 characters in body
Oct 15, 2012 at 16:22 comment added Steven Gubkin It might be more appropriate to remove the link to the paper, and just stick to the mathematical question. If it turns out there is an actual error in the paper, then the author could be contacted privately.
Oct 15, 2012 at 16:08 history asked palio CC BY-SA 3.0