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arXiv:0807.4248v1[math.GT]26Jul2008 EXOTIC STRUCTURES ON SMOOTH 4-MANIFOLDS
 

Summary: arXiv:0807.4248v1[math.GT]26Jul2008
EXOTIC STRUCTURES ON SMOOTH 4-MANIFOLDS
SELMAN AKBULUT
Abstract. A short survey of exotic smooth structutes on 4-manifolds is
given with a special emphasis on the corresponding cork structures. Along
the way we discuss some of the more recent results in this direction, obtained
jointly with R. Matveyev, B.Ozbagci, C.Karakurt and K.Yasui.
0. Corks
Let M be a smooth closed simply connected 4-manifold, and M
be an exotic
copy of M (a smooth manifold homeomorphic but not diffeomorphic to M).
Then we can find a compact contractible codimension zero submanifold W M
with complement N, and an involution f : W W giving a decomposition:
(1) M = N id W , M
= N f W
Figure 1.
The existence of this structure was first observed on an example in [A1], then
in [M] and [CFHS] it was generalized to the general form discussed above; and
another improved version was given in [K]. Since then the contractible pieces
W appearing in this decomposition has come to be known as "corks".

  

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

 

Collections: Mathematics