Volume 19, Issue 3

The Farrell-Jones and the Baum-Connes Conjecture say that one can compute the algebraic K - and L -theory of the group ring and the topological K -theory of the reduced group C *-algebra of a group G in terms of these functors for the virtually cyclic subgroups or the finite subgroups of G . By induction theory we want to reduce these families of subgroups to a smaller family, for instance to the family of subgroups which are either finite hyperelementary or extensions of finite hyperelementary groups with ℤ as kernel or to the family of finite cyclic subgroups. Roughly speaking, we extend the induction theorems of Dress for finite groups to infinite groups.

A parabolic Harnack inequality for the equation is proved; in particular, this implies a sharp two-sided estimate for the associated heat kernel. Our approach relies on the unitary equivalence between the Schrödinger operator and the weighted Laplacian when .

Using functional analytical and graph theoretical methods, we extend the results of [Kramar M. und Sikolya E.: Spectral properties and asymptotic periodicity of flows in networks. Math. Z. 249 (2005), 139–162] to more general transport processes in networks allowing space dependent velocities and absorption. We characterize asymptotic periodicity and convergence to an equilibrium by conditions on the underlying directed graph and the (average) velocities.

A classical problem in algebraic deformation theory is whether an infinitesimal deformation can be extended to a formal deformation. The answer to this question is usually given in terms of Massey powers. If all Massey powers of the cohomology class determined by the infinitesimal deformation vanish, then the deformation extends to a formal one. We consider another approach to this problem, by constructing a miniversal deformation of the algebra. One advantage of this approach is that it answers not only the question of existence, but gives a construction of an extension as well.

In this paper we use the technique of pulling back global Bessel models via the theta correspondence to prove two theorems.

We characterize H -spaces which are p -torsion Postnikov pieces of finite type by a cohomological property together with a necessary acyclicity condition. When the mod p cohomology of an H -space is finitely generated as an algebra over the Steenrod algebra we prove that its homotopy groups behave like those of a finite complex. In particular, a p -complete infinite loop space has a finite number of non-trivial homotopy groups if and only if its mod p cohomology satisfies this finiteness condition.

Two sets of conditions are presented for the compactness of a real plane algebraic curve, one sufficient and one necessary, in terms of the Newton polygon of the defining polynomial.