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Local and global topology of the CMB anisotropy
and polarization elds
I. D. Novikov et al.
Theoretical Astrophysics Center,Denmark
We discuss local and global topology of the anisotropy and
polarization elds in connection with the BOOMERANG and
MAXIMA-1 observational data. It is shown that the level of
cross-correlation between anisotropy and polarization increases
 times around -heigh isolated peaks of the anisotropy. This
kind of polarization has a local maximum of amplitude 30-40
percents around  = 3 peak, and is concentrated in a \ring"
around that peak. We make corresponding predictions for the fu-
ture polarization measurements by PLANCK around high peaks
at the MAXIMA-1 pixelized map. The cross-correlation between
anisotropy and polarization is a sensitive test to distinguish be-
tween the CMB signal and polarized point sources. The next top-
ics of our investigation are geometrical and statistical properties
of the polarization eld itself. Singular points of the CMB polar-
ization vector eld where the polarization vanishes, are found and
classied. It is shown that the ratio of numbers of such singular
points of dierent types on a map, and their clusterization are
crucial tests for the Gaussian nature of a signal on the map.
Co-authors: P.D.Naselsky and D.I.Novikov
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