ON THE CALCULATION OF UNIL
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Date
02/04/2003Author
Ranicki, Andrew
Connolly, Frank
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Abstract
Cappell’s codimension 1 splitting obstruction surgery group
UNiln is a direct summand of the Wall surgery obstruction group of an
amalgamated free product. For any ring with involution R we use the
quadratic Poincar´e cobordism formulation of the L-groups to prove that
Ln(R[x]) = Ln(R) (+) UNiln(R;R,R) .
We combine this with M. Weiss’ universal chain bundle theory to pro-
duce almost complete calculations of UNil.(Z; Z,Z) and theWall surgery
obstruction groups L.(Z[D1]) of the infinite dihedral group D1 =
Z2 * Z2. Our main results are stated in 0.2.