In this paper we prove that for every bumpy Finsler metric F on every rationally homological n-dimensional sphere Sn with n ≥ 2, there exist always at least two distinct prime closed geodesics.

Connes and Cuntz showed in [Comm. Math. Phys. 114 (1988), 515–526] that suitable cyclic cocycles can be represented as Chern characters of finitely summable semifinite Fredholm modules. We show an analogous result in twisted cyclic cohomology using Chern characters of modular Fredholm modules. We present examples of modular Fredholm modules arising from Podleś spheres and from SUq(2).

We recognize the Gromoll-Meyer sphere Σ as the geodesic join of a simple closed geodesic and a minimal subsphere Σ ⊂ Σ, which can be equivariantly identified with the Brieskorn sphere W 5 3 . As applications we in particular determine the full isometry group of Σ, classify all closed subgroups which act freely, determine the homotopy types of the corresponding orbit spaces, identify the Hirsch-...

We will announce some results on the values of quantum sl2 invariants of knots and integral homology spheres. Lawrence’s universal sl2 invariant of knots takes values in a fairly small subalgebra of the center of the h-adic version of the quantized enveloping algebra of sl2 . This implies an integrality result on the colored Jones polynomials of a knot. We define an invariant of integral homolo...

Durhuus and Jonsson (1995) introduced the class of “locally constructible” (LC) 3-spheres and showed that there are only exponentially-many combinatorial types of simplicial LC 3-spheres. Such upper bounds are crucial for the convergence of models for 3D quantum gravity. We characterize the LC property for d-spheres (“the sphere minus a facet collapses to a (d − 2)-complex”) and for d-balls. In...

We examine a recent argument that " identical " quantum particles with an anti-symmetric state (fermions) are weakly discernible objects, just like irreflexively related ordinary objects in situations with perfect symmetry (Black's spheres, for example). We conclude that the argument uses a silent premise that is not justified in the quantum case. 1 Individuality Objects are individuals. One mi...

A Dehn sphere Σ [P] in a closed 3-manifold M is a 2-sphere immersed in M with only double curve and triple point singularities. The sphere Σ fills M [Mo2] if it defines a celldecomposition of M . The inverse image in S of the double curves of Σ is the Johansson diagram of Σ [J1] and if Σ fills M it is possible to reconstruct M from the diagram. A Johansson representation of M is the Johansson d...

This paper analyzes the transformation of media structures and possible effects on public communication from 1960 to 2008. To build a basis for the evaluation of trends and situations in the various models of media and politics (Hallin/Mancini 2004), this paper will systematically analyze and compare the cases of Austria, Germany, and Switzerland (democratic-corporatist), Great Britain (liberal...