In mathematics, a symmetric obstruction theory, introduced by Kai Behrend, is a perfect obstruction theory together with nondegenerate symmetric bilinear form.
Example: Let f be a regular function on a smooth variety (or stack). Then the set of critical points of f carries a symmetric obstruction theory in a canonical way.
Example: Let M be a complex symplectic manifold. Then the (scheme-theoretic) intersection of Lagrangian submanifolds of M carries a canonical symmetric obstruction theory.