For a metric \begin{align*} d s^{2}=\sum_{i=1}^{p} d x_{i}^{2}-\sum_{j=1}^{q} d t_{j}^{2} ,\end{align*} the signature is \((p, q)\).
signature
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Rohklin's theorem
If \(X^4\) is a smooth closed spin manifold (so \(w_2(X) = 0\)), then the signature of the intersection form is divisible by 16.
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E8 lattice
The lattice \(E_{8}\) is even, unimodular and of signature \((0,8)\).
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2022-03-28
Complex ball quotients, new symplectic 4-manifolds with nonnegative signature, Sümeyra Sakall, UGA topology seminar.