On the calculation of UNil

الأصل · EN

Cappell's codimension 1 splitting obstruction surgery group UNilₙ(R;R,R) of a ring with involution R is a direct summand of the Wall surgery obstruction group Lₙ(R[D∞]) of the amalgamated free product R[D∞] = R[Z₂]*ᵣR[Z₂], with D∞=Z₂*Z₂ the infinite dihedral group. We use the quadratic Poincaré cobordism formulation of the L-groups to prove that Lₙ(R[x]) = Lₙ(R)⊕ UNilₙ(R;R,R), with x = x. We combine this with M. Weiss' universal chain bundle theory to produce almost complete calculations of UNil*(Z;Z,Z) and L*(Z[D∞]).