Talk:Thom conjecture
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Attribution
[edit]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
[edit]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)