 
Summary: PROCEEDINGS OF THE
AMERICAN MATHEMATICAL SOCIETY
Volume 53, Number 2, December 1975
E Q U I V A L E N C E O F 5DIMENSIONAL sCOBORDISMS
MARTIN SCHARLEhlANN
ABSTRACT. The classification of 5dimensional hcobordisms given
by Cappell, Lashof, and Shaneson i s here strengthened and extended to
scobordisms when the ends of the scobordism are smooth.
1. Introduction. An scobordism between compact manifolds M and M'
will b e an scobordism which restricts to a product cobordism between dW
and dM1. Two scobordisms W and W' from a compact 4manifold to a smooth
manifold are equivalent if there are smooth Scobordisms V and V' with d2W
= d l V , d2w1= d l v l and a homeomorphism of W u V onto W' u V ' which i s
the identity on +I = ddlW and a diffeomorphism from d2V to d 2 V 1 . Given a
smooth 4manifold .M, let ,Mk denote the connected sum of M and k copies
of s2 x s2.
Theorem. There i s a k such that for any connected compact smooth
