Great post; I need to write up my own introductory and elementary explanation of this.
I have an update on the subject of a post I wrote several months ago, in which I used the word “wormhole” together with the following graphic as a shameless attention-getting device:
(It worked then, so why not use it now?)
Anyway, topologists know that when I say wormhole, I mean connected sum: the topic of that earlier post was the fact that the prime decomposition theorem for tight contact 3-manifolds cannot be extended to dimension five, or to put it another way, nonprime 5-manifolds can admit strictly more tight contact structures than what you would get just by performing contact connected sums. Examples of this were observed in the second version of my preprint with Paolo Ghiggini and Klaus Niederkrüger, inspired in part by a result of Bowden, Crowley and Stipsicz, which I’ll have more to say about below.
The new development…
View original post 1,688 more words