Timeline for Topological obstructions to existence of immersion

6 events

when toggle format	what		by	license	comment
Jul 10, 2018 at 20:53	history	edited	Ian Agol	CC BY-SA 4.0	added 2646 characters in body
Jun 23, 2018 at 6:30	comment	added	Ian Agol		Yes, the Whitehead manifold (and in fact any contractible 3-manifold other than $\mathbb{R}^3$) cannot cover a compact 3-manifold. However, it embeds in $S^3$, and I wouldn't be surprised if other contractible 3-manifolds immerse in $S^3$. The point of this answer is that in the 2-dimensional case, one can say something stronger than (c) (but weaker than (a)).
Jun 23, 2018 at 6:21	comment	added	H1ghfiv3		Thank you very much for this elaborate and illuminating answer. I believe that there exist open manifolds of dimension $\geq 3$ that do not cover any compact manifold (doesn't the whitehead manifold have this property ?).
Jun 22, 2018 at 23:53	history	edited	Ian Agol	CC BY-SA 4.0	added 152 characters in body
Jun 22, 2018 at 23:10	comment	added	Ian Agol		I think I can answer the nonorientable case now too, which involves cubic graphs with perfect matchings, but has a little complication due to torsion. I’ll try to write something.
Jun 22, 2018 at 19:14	history	answered	Ian Agol	CC BY-SA 4.0