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) modulo 4. We
use n_{lambda}(f) 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 formulas for n_{lambda}(f). 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.