Positive index of the intersection form
= Positive index of the intersection form
{title2=$b_2^+(X)$}
For a closed oriented <smooth four-manifold>, $b_2^+$ is the dimension of a maximal positive-definite subspace of its real <intersection form>. A <symplectic form> forces $b_2^+\geq1$, because its <cohomology class> has positive square. Reversing orientation exchanges the positive and negative indices.