The Mudcat Café TM
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 in Pacific Journal of Mathematics 217 (2004), 291-302. I mean, this is cool stuff!