 
Summary: PROCEEDINGS OF THE
AMERICAN MATHEMATICAL SOCIETY
Volume 00, Number 0, Xxxx XXXX, Pages 000000
S 00029939(XX)00000
DECOMPOSING A 4MANIFOLD
SELMAN AKBULUT
(Communicated by Ronald Fintushel)
Abstract. A splitting of a manifold in Kirby's problem list (no.4.97) is given
Gauge theory provides many fake copies of oriented closed smooth manifolds X
with b+
2 (X) odd. Unfortunately, there is no such example with b+
2 (X) even. In
problem 4.97 of Kirby's problem list [4] the author suggested possible a candidate
for such an example. Here we show that our example fails to be fake. Along the way
we show some interesting splittings of Milnor fibers of some Brieskorn singularities.
Let Q be the Milnor fiber of z2
1 + z3
2 + z13
3 . In particular Q is the homology
sphere = (2, 3, 13), and Q is a simply connected spin 4manifold with signature
