# Topology Seminar: Rob Schneiderman (Lehman College CUNY) "Extending Gabai's general 4-dimensional Light Bulb Theorem"

Date and time:
Room 304 Boyd

Abstract: David Gabai's smooth general 4-dimensional Light Bulb Theorem states roughly that `for embedded 2-spheres in an orientable 4-manifold, homotopy implies isotopy, in the presence of a geometric dual sphere and the absence of 2-torsion in the ambient fundamental group'. In joint work with Peter Teichner this result is extended to arbitrary orientable 4-manifolds by showing that an invariant of Mike Freedman and Frank Quinn which takes values in a quotient of the Z/2Z-vector space on the 2-torsion fundamental group elements gives the complete obstruction to the existence of an isotopy between homotopic embedded 2-spheres having a common geometric dual. We also give an alternative approach to Gabai's proof.