Algebraic surgery X (Ex)
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Let be a degree one normal map of -GPC. Denote by , the respective SNFs. We form the -dimensional geometric (normal,~Poincar\'e) pair
with . The symbol denotes the -spherical fibration over induced by and
is the map induced by and and denote .
Let be the underlying chain complex obtained by algebraic surgery on the -dimensional symmetric pair
Show that it is homotopy equivalent to the mapping cone of the 'Umkehr' map associated to .