Thread #59418 Message #1915289

Posted By: Rapparee

20-Dec-06 - 08:50 PM

Thread Name: BS: The Mother of all BS threads

Subject: RE: BS: The Mother of all BS threads

Now, THIS is cool!

RELATIVE TOPOLOGY OF REAL ALGEBRAIC

VARIETIES IN THEIR COMPLEXIFICATIONS

Yildiray Ozan

We investigate, for a given smooth closed manifold M, the

existence of an algebraic model X for M (i.e., a nonsingular

real algebraic variety diffeomorphic to M) such that some

nonsingular projective complexification i : X → XC of X

admits a retraction r : XC → X. If such an X exists, we

show that M must be formal in the sense of Sullivan's minimal

models, and that all rational Massey products on M are

trivial.

We also study the homomorphism on cohomology induced

by i for algebraic models X of M. Using ´etale cohomology, we

see that mod p Steenrod powers give an obstruction for the

induced map on cohomology, i∗ : Hk(XC, Zp) → Hk(X, Zp), to

be onto, if we require that X is defined over rational numbers.

You'll want to read the entire article inPacific Journal of Mathematics217 (2004), 291-302. I mean, this is cool stuff!