Novikov-Shubin Signatures, I

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Torsion objects of von Neumann categories describe the phenomenon "spectrum near zero" discovered by Novikov and Shubin. In this paper we classify Hermitian forms on torsion objects of a finite von Neumann category. We prove that any such Hermitian form can be represented as the discriminant form of a degenerate Hermitian form on a projective module. We also find the relation between the Hermitian forms on projective modules which holds if and only if their discriminant forms are congruent. A notion of superfinite von Neumann category is introduced. It is proven that the classification of torsion Hermitian forms in a superfinite category can be completely reduced to the isomorphism types of their positive and the negative parts.

Original languageEnglish
Pages (from-to)477-515
Number of pages39
JournalAnnals of Global Analysis and Geometry
Issue number5
StatePublished - 2000


  • Extended L cohomology
  • Hermitian forms
  • Von Neumann categories


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