5 papers · 1 filter
Concordance of spheres in 4-manifolds with an immersed dual sphere
Michael Klug, Maggie Miller
Let and be two homotopic, oriented 2-spheres embedded in an orientable 4-manifold . After discussing several operations for modifying an immersion of a 3-manifold in…
Kernels of splitting homomorphisms
Michael R. Klug
Lei and Wu have given a description of the second homotopy group of a closed orientable 3-manifold in terms of the kernels of the epimorphisms from the fundamental group of a Heega…
Building Groups From Restricted Diagrams of Groups
Nic Brody, Michael R. Klug
We consider the problem of realizing a group as the fundamental group of a graph of groups where the vertex groups are restricted to certain classes (for example, coming from a cer…
A relative version of Rochlin's theorem
Michael R. Klug
Rochlin proved that a closed 4-dimensional connected smooth oriented manifold with vanishing second Stiefel-Whitney class has signature divisible by 16. This was gener…
Representing smooth 4-manifolds as loops in the pants complex
Gabriel Islambouli, Michael Klug
We show that every smooth, orientable, closed, connected 4-manifold can be represented by a loop in the pants complex. We use this representation, together with the fact that the p…