Twisted L^2 invariants of non-simply connected manifolds
Abstract
We develop the theory of twisted L^2-cohomology 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^2-cohomology 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 1-form is exact. We define the extended twisted L^2 de Rham cohomology and prove the asymptotic L^2 Morse-Farber inequalities, which give quantitative lower bounds for the Morse numbers of a Morse 1-form on M.
Keywords
Cite
@article{arxiv.dg-ga/9610018,
title = {Twisted L^2 invariants of non-simply connected manifolds},
author = {Varghese Mathai and Mikhail Shubin},
journal= {arXiv preprint arXiv:dg-ga/9610018},
year = {2008}
}
Comments
AMS-LaTeX v1.2, 28 pages, to appear in special issue of Russ.Jour.of Math.Physics