# Seminars & Events for Topology Seminar

##### The total surgery obstruction

**Please note special time. **The 1960's Browder-Novikov-Sullivan-Wall high-dimensional surgery theory for deciding if an n-dimensional Poincare duality space X is homotopy equivalent to an n-dimensional topological manifold has two obstructions. There is a primary topological K-theory obstruction to the existence of a topological bundle structure on the Spivak spherical fibration \nu{X \subset S^{n+k}}. There is also a secondary algebraic L-theory surgery obstruction in the Wall group L_n(Z[\pi_1(X)]) of quadratic forms over the fundamental group ring Z[\pi_1(X)], which depends on the resolution of the primary obstruction. In 1979 (in Princeton) I united these two obstructions in a single "total surgery obstruction" s(X) \in S_n(X).