Abstract
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 L 2 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.
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Farber, M. Novikov–Shubin Signatures, II. Annals of Global Analysis and Geometry 19, 259–291 (2001). https://doi.org/10.1023/A:1010712528051
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DOI: https://doi.org/10.1023/A:1010712528051