  Given a mapping class f of an oriented surface Sigma and a lagrangian lambda
in the first homology of Sigma, we define an integer n_{lambda}(f). We use
n_{lambda}(f) (mod 4) to describe a universal central extension of the mapping
class group of Sigma as an index-four subgroup of the extension constructed
from the Maslov index of triples of lagrangian subspaces in the homology of the
surface. We give two descriptions of this subgroup. One is topological using
surgery, the other is homological and builds on work of Turaev and work of
Walker. Some applications to TQFT are discussed. They are based on the fact
that our construction allows one to precisely describe how the phase factors
that arise in the skein theory approach to TQFT-representations of the mapping
class group depend on the choice of a lagrangian on the surface.
