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∞=Z2*Z2, extending the results of Connolly and Ranicki [Adv. Math. 195 (2005) 205–258], Connolly and Davis [Geom. Topol. 8 (2004) 1043–1078, e-print http://arXiv.org/abs/math/0306054].