Twisted L2 Invariants of Non-simply Connected Manifolds and Asymptotic L2 Morse Inequalities
نویسندگان
چکیده
We develop the theory of twisted L-cohomology and twisted spectral invariants for flat Hilbertian bundles over compact manifolds. They can be viewed as functions on H(M, R) and they generalize the standard notions. A new feature of the twisted L-cohomology theory is that in addition to satisfying the standard L Morse inequalities, they also satisfy certain asymptotic L 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 de Rham cohomology and prove the asymptotic L Morse-Farber inequalities, which give quantitative lower bounds for the Morse numbers of a Morse 1-form on M .
منابع مشابه
1 99 6 Twisted L 2 Invariants of Non - Simply Connected Manifolds and Asymptotic L 2 Morse Inequalities
We develop the theory of twisted L-cohomology and twisted spectral invariants for flat Hilbertian bundles over compact manifolds. They can be viewed as functions on H(M, R) and they generalize the standard notions. A new feature of the twisted L-cohomology theory is that in addition to satisfying the standard L Morse inequalities, they also satisfy certain asymptotic L Morse inequalities. These...
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