Grasper families of spheres in $S^2\times D^2$ and barbell diffeomorphisms of $S^1\times S^2\times I$

Eduardo Fernández, David T. Gay, Daniel Hartman +1

We show that the fundamental group of framed circles in $S^1\times D^3$ injects into the fundamental group of framed spheres in $S^2\times D^2$, so that the cokernel is the fundam…