when i read Milnor's famous book topology from the differential view point, in the chapter framed cobordism and Pontyagin construction ,he says that :suppose that $f$:M$\rightarrow$ $S^{p}$ is smooth,where dimM=p,then we can define the degree of $f$ ,and Milnor says that the framed cobordant 0- Pontryagin manifold are determinde by $\sum sgn(x)$ where x is in the framed cobordant 0-Pontryagin manifold. I know that framed cobordant 0- Pontryagin manifold have the same $\sum sgn(x)$, but i can't proof the inverse.