Novikov-Shubin Signatures, I

Research output: Contribution to journalArticlepeer-review

Abstract

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
Volume18
Issue number5
DOIs
StatePublished - 2000

Keywords

  • Extended L cohomology
  • Hermitian forms
  • Von Neumann categories

Fingerprint

Dive into the research topics of 'Novikov-Shubin Signatures, I'. Together they form a unique fingerprint.

Cite this