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In the first part of this paper, we propose a uniform interpretation of characteristic classes as obstructions to the reduction of the structure group and to the existence of an equivariant extension of a certain homomorphism defined a priori only on a sin ...
Internal fluid pressure often plays an important role in the rupture of brittle materials. This is a major concern for many engineering applications and for natural hazards. More specifically, the mechanisms through which fluid pressure, applied at a micro ...
We investigate the theory of principal bundles from a homotopical point of view. In the first part of the thesis, we prove a classification of principal bundles over a fixed base space, dual to the well-known classification of bundles with a fixed structur ...
At the typical spatial resolution of MRI in the human brain, approximately 60–90% of voxels contain multiple fiber populations. Quantifying microstructural properties of distinct fiber populations within a voxel is therefore challenging but necessary. Whil ...
The vast number of propagating solutions to the wave equation in multimode optical fibers represents a larger information capacity than provided by fiber bundles of the same diameter. Therefore, in the field of imaging, multimode fibers potentially allow t ...
Given a fiber bundle of GKM spaces, pi: M -> B, we analyze the structure of the equivariant K-ring of M as a module over the equivariant K-ring of B by translating the fiber bundle, pi, into a fiber bundle of GKM graphs and constructing, by combinatorial t ...
Every principal G-bundle over X is classified up to equivalence by a homotopy class X -> BG, where BG is the classifying space of G. On the other hand, for every nice topological space X Milnor constructed a strict model of its loop space (Omega) over tild ...
Let T be a torus and B a compact T-manifold. Goresky et al. show in [3] that if B is (what was subsequently called) a GKM manifold, then there exists a simple combinatorial description of the equivariant cohomology ring H-T*(B) as a subring of H-T*(B-T). I ...
We study equations on a principal bundle over a compact complex manifold coupling a connection on the bundle with a Kahler structure on the base. These equations generalize the conditions of constant scalar curvature for a Kahler metric and Hermite-Yang-Mi ...
In this paper we obtain parametrizations of the moduli space of principal bundles over a compact Riemann surface using spaces of Hecke modifications in several cases. We begin with a discussion of Hecke modifications for principal bundles and give construc ...
