 
Summary: CAPPELLSHANESON'S 4DIMENSIONAL SCOBORDISM
SELMAN AKBULUT
0. Introduction
Let Q3
= S3
/Q8 be the quaternionic 3manifold, obtained as the quotient of the
3sphere by the free action of the quaternionic group Q8 of order eight, which can
be presented by Q8 =< i, j, k  i2
= j2
= k2
= 1, ij = k, jk = i, ki = j >. Also
Q is the 2fold branched covering space of S3
branched over the three Hopf circles;
combining this with the Hopf map S3
S2
one sees that Q is a Seifert Fibered space
with three singular fibers. Q is also the 3fold branched covering space of S3
branched
over the trefoil knot. Q can also be identified with the boundaries of the 4manifolds
of Figure 1 (one can easily check that the above three definitions are equivalent to this
