Vol. 102, No. 1, 1982

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The exact sequence of a localization for Witt groups. II. Numerical invariants of odd-dimensional surgery obstructions

William Leslie Pardon

Vol. 102 (1982), No. 1, 123–170

The propose of this paper is to define numerical invariants of odd-dimensional surgery obstructions, computable in a way similar to that used to compute the index and Arf invariants of even-dimensional surgery obstructions. The main result is that a system of integral congruences (“numerical invariants”) suffices, modulo the projective class group, to determine whether or not an odd-dimensional surgery obstruction vanishes, when the fundamental group is a finite 2-group. In addition, the numerical invariants turn out to be Euler characteristics in certain cases of topological interest, including the existence of product formulas.

Mathematical Subject Classification 2000
Primary: 57R67
Secondary: 10C05
Received: 3 January 1979
Published: 1 September 1982
William Leslie Pardon