Tuesday, March 12, 2013

Manolescu's new result on the triangulation conjecture

Ciprian Manolescu has a new paper on the archive  http://arxiv.org/abs/1303.2354

There he settles the longstanding  triangulation conjecture: in any dimension $n>3$ there exist nontriangulable compact topological manifolds. The approach is  the one opened in the  1980 by the Gaweski-Stern  Annals paper where they pointed out the relationship between this  conjecture and the existence of homology 3-spheres with Rochlin invariant  1 and having order two in the homology cobordism group.

This  new result of Manolescu is  big news indeed, provided that the details of the proof turn out  OK. As for the method, he goes back to his, not so distant, youth.