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Summary: CAPPELL-SHANESON'S 4-DIMENSIONAL S-COBORDISM
SELMAN AKBULUT
0. Introduction
Let Q3
= S3
/Q8 be the quaternionic 3-manifold, obtained as the quotient of the
3-sphere 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 2-fold 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 3-fold branched covering space of S3
branched
over the trefoil knot. Q can also be identified with the boundaries of the 4-manifolds
of Figure 1 (one can easily check that the above three definitions are equivalent to this
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