English

Smooth structures on collarable ends of 4-manifolds

dg-ga 2008-02-03 v1 Differential Geometry

Abstract

We use Furuta's result, usually referred to as ``10/8-conjecture'', to show that for any compact 3-manifold MM the open manifold M\times\r has infinitely many different smooth structures. Another consequence of Furuta's result is existence of infinitely many smooth structures on open topological 4-manifolds with a topologically collarable end, provided there are only finitely many ends homeomorphic to it. We also show that for each closed spin 4-manifold there are exotic \rf's that can not be smoothly embedded into it.

Keywords

Cite

@article{arxiv.dg-ga/9604007,
  title  = {Smooth structures on collarable ends of 4-manifolds},
  author = {Zarko Bizaca and John Etnyre},
  journal= {arXiv preprint arXiv:dg-ga/9604007},
  year   = {2008}
}

Comments

8 pages, AMSTeX, no figures

R2 v1 2026-07-22T12:29:48.298Z