Generalized Arf invariants in algebraic L-theory

The difference between the quadratic L-groups L_(A) and the symmetric L-groups L^(A) of a ring with involution A is detected by generalized Arf invariants. The special case A=Z[x] gives a complete set of invariants for the Cappell UNil-groups UNil_(Z;Z,Z) for the infinite dihedral group D_{\infty}=Z_2Z_2, extending the results of Connolly and Ranicki (math.AT/0304016) and Connolly and Davis.