Seminars & Events for Algebraic Topology Seminar

April 30, 2015
4:30pm - 5:30pm
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).

Speaker: Andrew Ranicki, University of Edinburgh
Fine Hall 314