An open collar theorem for 4-manifolds

Abstract

Let M 4 {M^4} be an open 4 4 -manifold with boundary. Conditions are given under which M 4 {M^4} is homeomorphic to ∂ M × [ 0 , 1 ) \partial M \times [0,1) . Applications include a 4 4 -dimensional weak h h -cobordism theorem and a classification of weakly flat embeddings of 2 2 -spheres in S 4 {S^4} . Specific examples of ( n − 2 ) (n - 2) -spheres embedded in S n {S^n} (including n = 4 n = 4 ) are also discussed.