Abstract
We say that a topologically embedded 3-sphere in a smoothing of Euclidean
4-space is a barrier provided, roughly, no diffeomorphism of the 4-manifold
moves the 3-sphere off itself. In this paper we construct infinitely many one
parameter families of distinct smoothings of 4-space with barrier 3-spheres.
The existence of barriers implies, amongst other things, that the isometry
group of these manifolds, in any smooth metric, is finite. In particular, S^1
can not act smoothly and effectively on any smoothing of 4-space with barrier
3-spheres.
Users
Please
log in to take part in the discussion (add own reviews or comments).