Abstract
Torsion objects of von Neumann categories describe thephenomenon “spectrum near zero” discovered by Novikov and Shubin. Inthis paper we classify Hermitian forms on torsion objects of a finitevon Neumann category. We prove that any such Hermitian form can berepresented as the discriminant form of a degenerate Hermitian form on aprojective module. We also find the relation between the Hermitian formson projective modules which holds if and only if their discriminantforms are congruent. A notion of superfinite von Neumann category isintroduced. It is proven that the classification of torsion Hermitianforms in a superfinite category can be completely reduced to theisomorphism types of their positive and the negative parts.
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Farber, M. Novikov–Shubin Signatures, I. Annals of Global Analysis and Geometry 18, 477–515 (2000). https://doi.org/10.1023/A:1006653606519
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DOI: https://doi.org/10.1023/A:1006653606519