  In this paper, we propose a mathematical definition of a new ``numerical
invariants" of Calabi--Yau 3-folds from stable sheaves of dimension one, which
is motivated by the Gopakumar-Vafa conjecture in M-theory. Moreover, we show
that for any projective morphism $f:X -> Y$ of normal projective varieties,
there exists a natural $sl_2 \times sl_2$ action on the intersection cohomology
group $IH(X, \Q)$ which fits into the perverse Leray spectral sequence.
