I was really trying to understand this answer, but now need to get some other work done outside MathOverflow.

I deleted my previous comment so as not to confuse others. This logic puzzle is already confusing enough.

@Michael: it's not terribly clear from what you've written here what you are so upset about, but I'm sure everything will be fine if you just treat these mice fairly. I imagine these are grown-up mice you are talking about.

Wouldn't Whitney embedding theorem need 6 dimensions? Am I missing something? Wikipedia says you start with an immersion with transverse self-intersections, then you fix this. (I paraphrase.)

I wonder if someone would add here the reference for the Freedman result. Thanks!

I imagine in 6 you meant to say "the restriction to the boundary is isotopic to the identity". Interesting question!

While this isn't so clear from the title of the question, the first sentence in the text of the question mentions wanting things outside of pure mathematics.

I think the OP also wants the first homology group to be 0 -- going by the title of the question rather than the text.

I wonder if you would be willing to explain a little more how these wild arcs work -- I don't like opening links on the web, and I'm having a little trouble understanding your question without reading the Siebenmann manuscript. Thanks! Anyway, perhaps you'll get more answers to your question if you explain the question a little more.

@Justin: good luck with your work on this difficult question!

That's interesting! In case you edit your answer again, I think MacPherson has a capital "P".

I don't know the answer to your math question, but you don't sound at all like an idiot.

What is the definition of "wild" in this context? Thanks in advance for your help in understanding the answer!