Timeline for Are "Unions" of small exotic $\mathbb{R}^4$'s small?

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Jan 22, 2015 at 12:47	comment	added	drunken_monkey		Yes that is how I meant it, only additionally $U$ $V$ are also assumed to be homeomorphic to $\mathbb{R}^4$. I considered them both as submanifolds of a manifold $M$, but if one puts it like you, that's not necessary.
Jan 22, 2015 at 1:18	comment	added	Danny Ruberman		I don't think I understood your question, then. Perhaps you mean something like this: Suppose that there is a manifold $W$, homeomorphic to $R^4$, that is the union of two open submanifolds $U$ and $V$, such that $U \cap V$ is also homeomorphic to $R^4$, and each of $U$ and $V$ embeds in $R^4$. Then are you asking if $W$ embeds. Is that correct?
Jan 21, 2015 at 16:53	comment	added	drunken_monkey		Thank you for for your answer. This is what you could do if $U$ and $V$ are disjoint. I was rather interested in the case where their intersection is topologically "like an end sum", but not smoothly. $U \cap V$ could also be exotic itself and then I dont see how the argument should work.
Jan 21, 2015 at 16:20	history	answered	Danny Ruberman	CC BY-SA 3.0