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Linear direct connections

Jan Kubarski, Nicolae Teleman (2007)

Banach Center Publications

In this paper we study the geometry of direct connections in smooth vector bundles (see N. Teleman [Tn.3]); we show that the infinitesimal part, ∇ τ , of a direct connection τ is a linear connection. We determine the curvature tensor of the associated linear connection ∇ τ . As an application of these results, we present a direct proof of N. Teleman’s Theorem 6.2 [Tn.3], which shows that it is possible to represent the Chern character of smooth vector bundles as the periodic cyclic homology class of a...

Localization of basic characteristic classes

Dirk Töben (2014)

Annales de l’institut Fourier

We introduce basic characteristic classes and numbers as new invariants for Riemannian foliations. If the ambient Riemannian manifold M is complete, simply connected (or more generally if the foliation is a transversely orientable Killing foliation) and if the space of leaf closures is compact, then the basic characteristic numbers are determined by the infinitesimal dynamical behavior of the foliation at the union of its closed leaves. In fact, they can be computed with an Atiyah-Bott-Berline-Vergne-type...

Modular classes of Q-manifolds: a review and some applications

Andrew James Bruce (2017)

Archivum Mathematicum

A Q-manifold is a supermanifold equipped with an odd vector field that squares to zero. The notion of the modular class of a Q-manifold – which is viewed as the obstruction to the existence of a Q-invariant Berezin volume – is not well know. We review the basic ideas and then apply this technology to various examples, including L ∞ -algebroids and higher Poisson manifolds.

New sheaf theoretic methods in differential topology

Michael Weiss (2008)

Archivum Mathematicum

The Mumford conjecture predicts the ring of rational characteristic classes for surface bundles with oriented connected fibers of large genus. The first proof in [11] relied on a number of well known but difficult theorems in differential topology. Most of these difficult ingredients have been eliminated in the years since then. This can be seen particularly in [7] which has a second proof of the Mumford conjecture, and in the work of Galatius [5] which is concerned mainly with a “graph” analogue...

Currently displaying 161 – 180 of 346