Annals of Global Analysis and Geometry

, Volume 19, Issue 3, pp 259–291 | Cite as

Novikov–Shubin Signatures, II

  • M. Farber


This paper continues the author's previous paper, published inAnn. Global Anal. Geom.18 (2000), 477–515. Here weconstruct a linking form on the torsion part of middle-dimensionalextended L2 homology and cohomology of odd-dimensionalmanifolds. We give a geometric necessary condition when this linkingform is hyperbolic. We compute this linking form in case, when themanifold bounds. We introduce and study new numerical invariants of thelinking form: the Novikov–Shubin signature and the torsion signature;we compute these invariants explicitly for manifolds withπ1 = Z in terms of the Blanchfield form. We develop anotion of excess for extensions of torsion modules and show how thisconcept can be used to guarantee vanishing of the torsion signature.

extended L2 cohomology Hermitian forms von Neumann categories 


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© Kluwer Academic Publishers 2001

Authors and Affiliations

  • M. Farber
    • 1
  1. 1.Department of MathematicsTel Aviv UniversityTel AvivIsrael

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