 
Summary: NASH HOMOTOPY SPHERES ARE STANDARD
SELMAN AKBULUT
Abstract. We prove that the infinite family of homotopy 4spheres
constructed by Daniel Nash are all diffeomorphic to S4
.
0. Introduction
In [D], D.Nash constructed an infinite family of smooth homotopy
4spheres p,q,r,s indexed by (p, q, r, s) Z4
, and conjectured that they
are possibly not diffeomorphic to S4
. Here we prove that they are all
diffeomorphic to S4
. In spirit, Nash's construction is an easier version
of the construction of the AkhmedovPark in [AP], namely one starts
with a standard manifold X4
= X1 X2 which is a union of two basic
pieces along their boundaries, then does the "log transform" operations
to some imbedded tories in both sides with the hope of getting an
exotic copy of a known manifold M4
. In Nash's case X is the double
