Talk:Thom conjecture

Attribution

I reverted an edit stating that Thom denied the conjecture was his own. It would be great if someone could find a citation for such a statement. Orthografer 04:34, 20 March 2007 (UTC)

A bit puzzled by the wording

The article states:

"There are proofs for this conjecture in certain cases such as when Σ has nonnegative self intersection number, and assuming this number is nonnegative, this generalizes to Kähler manifolds (an example being the complex projective plane). It was first proved by Kronheimer-Mrowka and Morgan-Szabó-Taubes in October 1994, using the then-new Seiberg-Witten invariants."

Up to this point, the only ambient manifold discussed is CP², whose integer cohomology ring is merely the truncated polynomial ring given by Z[α] / (α³), where the generator α is a 2-dimensional cohomology class. Hence any nonzero 2-dimensional homology class Σ must have nonnegative self-intersection number.

So I am mystified by the initial part of the quoted sentence above up to the first comma. I mean, what other self-intersection number could be relevant in the case of CP² ?

So, the likelihood here is that the sentence should be reworded so that the part before the comma does not appear to refer to the CP² case. This should be done by someone who, unlike me, is familiar with the known theorems in this area.Daqu (talk) 21:22, 14 April 2010 (UTC)