# Do every 2 bulls embedded in \$ mathbb {R} ^ 4 \$ join a compact of \$ 3 \$?

Leave $$M subset mathbb {R} ^ 4$$ a compact submanifold imbibed diffeomorph for $$T ^ 2 = S ^ 1 times S ^ 1$$.

Is there always a compact subcompact? $$N subset mathbb {R} ^ 4$$ with $$M = N partial$$?

If so, it is $$N$$ always a solid bull $$S ^ 1 times D ^ 2$$?