  In this note we introduce and study a new class of maps called oriented
colored broken submersions. This is the simplest class of maps that satisfies a
version of the b-principle and in dimension 2 approximates the class of
oriented submersions well in the sense that every oriented colored broken
submersion of dimension 2 to a closed simply connected manifold is bordant to a
submersion.
  We show that the Madsen-Weiss theorem (the standard Mumford Conjecture) fits
a general setting of the b-principle. Namely, a version of the b-principle for
oriented colored broken submersions together with the Harer stability theorem
and Miller-Morita theorem implies the Madsen-Weiss theorem.
