Smooth structures on collarable ends of 4-manifolds

Details Smooth structures on collarable ends of 4-manifolds Smooth structures on collarable ends of 4-manifolds

1996-04-26

arxiv.org/abs/dg-ga/9604007v1

Mathematics

Differential Geometry

8 pages, AMSTeX, no figures

Scientific paper

We use Furuta's result, usually referred to as ``10/8-conjecture'', to show that for any compact 3-manifold $M$ 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.

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