Eigenvalues and Holonomy

Losik classes for codimension-one foliations

Following Losik's approach to Gelfand's formal geometry, certain characteristic classes for codimension-one foliations coming from the Gelfand-Fuchs cohomology are considered. Sufficient conditions for non-triviality in terms of dynamical properties of generators of the holonomy groups are found. The non-triviality for the Reeb foliations is shown; this is in contrast with some classical theorems on the Godbillon-Vey class, e.g, the Mizutani-Morita-Tsuboi Theorem about triviality of the Godbillon-Vey class of foliations almost without holonomy is not true for the classes under consideration. I…

A note on generalized Dirac eigenvalues for split holonomy and torsion

We study the Dirac spectrum on compact Riemannian spin manifolds $M$ equipped with a metric connection $\nabla$ with skew torsion $T\inΛ^3 M$ in the situation where the tangent bundle splits under the holonomy of $\nabla$ and the torsion of $\nabla$ is of `split' type. We prove an optimal lower bound for the first eigenvalue of the Dirac operator with torsion that generalizes Friedrich's classical Riemannian estimate.

Survey on eigenvalues of the Dirac operator and geometric structures

We give a survey of results relating the restricted holonomy of a Riemannian spin manifold with lower bounds on the spectrum of its Dirac operator, giving a new proof of a result originally due to Kirchberg.

丛方法中的语境性、n-语境性以及完整群（holonomy）的作用

Contextuality in the Bundle Approach, n-Contextuality, and the Role of Holonomy

本文以测度丛形式化语境性，证明 Fine-Abramsky-Brandenburger 定理，提出 n-语境性层级，并通过 Markov 联络揭示语境性与标架丛完整群非平凡性的关系。