  We investigate recently proposed HP1 sigma-model embedding method aimed to
study the topology of SU(2) gauge fields. The HP1 based topological charge is
shown to be fairly compatible with various known definitions. We study the
corresponding topological susceptibility and estimate its value in the
continuum limit. The geometrical clarity of HP1 approach allows to investigate
non-perturbative aspects of SU(2) gauge theory on qualitatively new level. In
particular, we obtain numerically precise estimation of gluon condensate and
its leading quadratic correction. Furthermore, we present clear evidences that
the string tension is to be associated with global (percolating) regions of
sign-coherent topological charge. As a byproduct of our analysis we estimate
the continuum value of quenched chiral condensate and the dimensionality of
regions, which localize the lowest eigenmodes of overlap Dirac operator.
