Fibre bundles, springer

Quantum Fibre Bundles

An approach to construction of a quantum group gauge theory based on the quantum group generalisation of fibre bundles is reviewed.

Connections on Principal Fibre Bundles

Complete definitions and motivations are given for principal fibre bundles, connections on these, and associated vector bundles. The relationships between various concepts of differentiation in these settings are proved. Finally, we briefly give an outline of the theory of curvature in terms of connections.

Quantum Groups on Fibre Bundles

It is shown that the principle of locality and noncommutative geometry can be connnected by a sheaf theoretical method. In this framework quantum spaces are introduced and examples in mathematical physics are given. With the language of quantum spaces noncommutative principal and vector bundles are defined and their properties are studied. Important constructions in the classical theory of prin...

Distal Transformation Groups and Fibre Bundles

Exotic Smooth Structures on Topological Fibre Bundles

We use a variation of Hatcher’s construction to construct, rationally stably, all exotic smooth structures on smooth manifold bundles whose fibers have sufficiently large odd dimension (at least twice the base dimension q plus 3). We show that, rationally stably, such smooth structures are classified by a cohomology class in the total space and the relative higher Igusa-Klein (IK) torsion is eq...