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ON THE CALCULATION OF UNIL

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calcunil.pdf (333.1Kb)
Date
02/04/2003
Author
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.
URI
http://hdl.handle.net/1842/237
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