There is the general principle to consider a classical invariant of a closed Riemannian
manifold M and to define its analog for the universal covering M taking the action of the …

Suppose ̄M is a compact connected odd-dimensional manifold with boundary, whose
interior M comes with a complete hyperbolic metric of finite volume. We will show that the …

Bibliography Page 1 Bibliography [1] MF Atiyah, R. Bott: A Lefschetz fixed point formula for
elliptic complexes II. Applications, Ann. of Math. 88 (1968), 451–491. [2] MF Atiyah, VK Patodi …

A standing conjecture in $ L^ 2$-cohomology says that every finite $ CW $-complex $ X $ is
of $ L^ 2$-determinant class. In this paper, we prove this whenever the fundamental group …

Let $ M $ be a compact manifold. and $ D $ a Dirac type differential operator on $ M $. Let $
A $ be a $ C^* $-algebra. Given a bundle $ W $ of $ A $-modules over $ M $(with …

In this paper we study the problem of approximation of the $ L^ 2$-topological invariants by
their finite dimensional analogues. We obtain generalizations of the theorem of L\" uck …

Bordism, rho-invariants and the Baum–Connes conjecture Page 1 J. Noncommut. Geom. 1 (2007),
27–111 Journal of Noncommutative Geometry © European Mathematical Society Bordism …

Approximating L2-invariants by their classical counterparts Page 1 EMS Surv. Math. Sci. 3 (2016),
269–344 DOI 10.4171/EMSS/18 EMS Surveys in Mathematical Sciences © European …

We consider systems $(M,\omega, g) $ with $ M $ a closed smooth manifold, $\omega $ a
real valued closed one form and $ g $ a Riemannian metric, so that $(\omega, g) $ is a …

In this article we give a survey on open problems and conjectures concerning L^ 2-
invariants. We cover the whole portfolio and not only certain aspects as they are considered …