Twisted L^2 invariants of nonsimply connected manifolds
Abstract
We develop the theory of twisted L^2cohomology and twisted spectral invariants for flat Hilbertian bundles over compact manifolds. They can be viewed as functions on the first de Rham cohomology of M and they generalize the standard notions. A new feature of the twisted L^2cohomology theory is that in addition to satisfying the standard L^2 Morse inequalities, they also satisfy certain asymptotic L^2 Morse inequalities. These reduce to the standard Morse inequalities in the finite dimensional case, and when the Morse 1form is exact. We define the extended twisted L^2 de Rham cohomology and prove the asymptotic L^2 MorseFarber inequalities, which give quantitative lower bounds for the Morse numbers of a Morse 1form on M.
 Publication:

eprint arXiv:dgga/961001
 Pub Date:
 October 1996
 arXiv:
 arXiv:dgga/9610018
 Bibcode:
 1996dg.ga....10018M
 Keywords:

 Mathematics  Differential Geometry;
 58 (Primary)
 EPrint:
 AMSLaTeX v1.2, 28 pages, to appear in special issue of Russ.Jour.of Math.Physics