Timeline for Compact Complex n-folds with Betti numbers $b_1=b_2=b_n=0$ for $n >3$

11 events

when toggle format	what		by	license	comment
Dec 25, 2012 at 11:19	vote	accept	Andrew McHugh
Dec 25, 2012 at 1:09	answer	added	Dmitri Panov		timeline score: 10
Dec 24, 2012 at 0:33	history	edited	Andrew McHugh		edited tags
Dec 23, 2012 at 23:49	comment	added	Daniel Litt		@Andrew McHugh: Indeed, that is a well-known open question.
Dec 23, 2012 at 23:20	comment	added	Andrew McHugh		I edited the question to specify compact.
Dec 23, 2012 at 23:17	history	edited	Andrew McHugh	CC BY-SA 3.0	added 31 characters in body; edited title; edited title
Dec 23, 2012 at 21:55	comment	added	Andrew McHugh		I think you are right. I should have said homology 6-sphere instead of topological $S^6$. I believe it is still a well known open question as to whether $S^6$ has an integrable complex structure.
Dec 23, 2012 at 21:00	comment	added	Daniel Litt		@Andrew McHugh: Am I missing something? Isn't the $n=3$ case the question of whether a homology $6$-sphere admits a complex structure? Or is a homology $6$-sphere admitting a complex structure automatically $S^6$?
Dec 23, 2012 at 20:12	comment	added	Andrew McHugh		Yes, I should have put in compact.
Dec 23, 2012 at 18:14	comment	added	Jason Starr		Compact? Obviously there are non-compact examples.
Dec 23, 2012 at 17:50	history	asked	Andrew McHugh	CC BY-SA 3.0