Hypercomplex structures on Kähler manifolds

Let (M, I) be a compact K?hler manifold admitting a hypercomplex structure (M, I, J, K). We show that (M, I, J, K) admits a natural HKT-metric. This is used to construct a holomorphic symplectic form on (M, I). Received: August 2004 Revision: August 2004 Accepted: August 2004     

L 2-cohomology of negatively curved Kähler manifolds of finite volume

We compute the space of L² harmonic forms (outside the middle degrees) on negatively curved K?hler manifolds of finite volume. Received: June 2004 Revision: August 2004 Accepted: September 2004     

Floer Homology and the Heat Flow

We study the heat flow in the loop space of a closed Riemannian manifold M as an adiabatic limit of the Floer equations in the cotangent bundle. Our main application is a proof that the Floer homology of the cotangent bundle, for the Hamiltonian function kinetic plus potential energy, is naturally isomorphic to the homology of the loop space. J.W. received partial financial support from TH-Projekt 00321. Received: December 2004 Revision: September 2005 Accepted: September 2005     

On the nested refinement of quadrilateral and hexahedral finite elements and the affine approximation

Summary. It is shown in this paper that the optimal approximation property of bilinear or trilinear finite elements would be retained when the affine mapping is used to replace the Q₁ mapping on each element, if the grids are refined nestedly. The new method truncates the quadratic and cubic terms in reference mappings and produces constant Jacobians and Jacobian matrices. This would avoid a shortcoming of the quadrilateral and hexahedral elements where the integrals of rational functions have to be computed or approximated. Numerical tests verify the analysis.Mathematics Subject Classification (2000): 65N30, 65N50, 65N55Revised version received January 29, 2004     

On the kernel of the Gassner representation

We study the Gassner representation of the pure braid group P_n by considering its restriction to a free subgroup F. The kernel of the restriction is shown to lie in the subgroup [Γ³F, Γ²F], sharpening a result of Lipschutz.Received: 25 August 2004; revised: 1 November 2004