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Proceedings of 5th Geometry-Topology Conference,

Summary: Proceedings of 5th
Geometry-Topology Conference,
pp, 1 ­ 14
A Fake Cusp and a Fishtail
Selman Akbulut
Dedicated to Robion Kirby on the occasion of his 60'th birthday
Abstract. We construct smooth 4-manifolds that are homeomorphic but not diffeo-
morphic to the "cusp" and the "fishtail", which are thickened singular 2-spheres.
Even though many fake smoothings of 4-manifolds are known to exists, we know little
about the basic building blocks of exotic smooth manifolds. This is mainly due to the
fact that we still don't know if basic manifolds like S4
, S2
× S2
, and S1
× S3
could admit
fake smooth structures. Unable to show this, we demonstrate fake smooth structures on
manifolds that are in a way "small deformations" of S2
× B2


Source: Akbulut, Selman - Department of Mathematics, Michigan State University


Collections: Mathematics