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Characteristic classes for A -bundles

Cap, Andreas;  Schichl, Hermann — 1996

Proceedings of the Winter School "Geometry and Physics"

The authors generalize a construction of Connes by defining for an A -bundle E over smooth manifold X and a reduced cyclic cohomology class c a sequence of de Rham cohomology classes c h c k ( E ) . Here A is a convenient algebra, defined by the authors, and E is a locally trivial bundle with standard fibre a right finitely generated projective A -module and bounded A -modules homomorphisms as transition functions.

Global Gronwall estimates for integral curves on Riemannian manifolds.

Michael Kunzinger;  Hermann Schichl;  Roland Steinbauer;  James A. Vickers — 2006

Revista Matemática Complutense

We prove Gronwall-type estimates for the distance of integral curves of smooth vector fields on a Riemannian manifold. Such estimates are of central importance for all methods of solving ODEs in a verified way, i.e., with full control of roundoff errors. Our results may therefore be seen as a prerequisite for the generalization of such methods to the setting of Riemannian manifolds.

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