Agrarian and $L^2$-invariants

Twisted L2 Invariants of Non-simply Connected Manifolds and Asymptotic L2 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...

Boserup and Agrarian Ecology

Hilbertian versus Hilbert W*-modules, and Applications to L2- and Other Invariants

Hilbert(ian) A-modules over finite von Neumann algebras with a faithful normal trace state (from global analysis) and Hilbert W*-modules over A (from operator algebra theory) are compared, and a categorical equivalence is established. The correspondence between these two structures sheds new light on basic results in L-invariant theory providing alternative proofs. We indicate new invariants fo...

L2-Invariants and Their Applications to Geometry, Group Theory and Spectral Theory

During the last decades mathematics has developed at an incredible speed and a large amount of new information and results have been accumulated. Therefore mathematics faces the problem that it breaks up into different areas which may not communicate among one another. Fortunately recent developements go in the opposite direction. In particular interactions of different fields have turned out t...

Hilbert modules and modules over finite von Neumann algebras and applications to L2-invariants

Throughout this paper A is a finite von Neumann algebra and tr :A −→ C is a finite normal faithful trace. Recall that a von Neumann algebra is finite if and only if it possesses such a trace. Let l2(A) be the Hilbert space completion of A which is viewed as a pre-Hilbert space by the inner product 〈a, b〉 = tr(ab∗). A finitely generated Hilbert A-module V is a Hilbert space V together with a lef...