Algebraic L ‐Theory, II: Laurent Extensions

where Az = A[z, z ] is the Laurent extension ring of A, with involution z h> z~. (Cf. Part III, [5], for the generalization to twisted Laurent extensions.) Similar splittings arise in [3]—indeed, our method of proof follows that of [3], except that Novikov neglects 2-torsion in the Z-groups, and assumes that 2 is invertible in A. In the geometrically realizable case A = Z[TT], (TT a finitely presented group), it is possible to obtain the decompositions by topological methods ([2], [6], and [8]). Defining X-theories L^^A) for m < 2, n (mod 4) by