Geometric decompositions of 4-dimensional orbifold bundles

Geometric Decompositions of 4-dimensional Orbifold Bundles

We consider geometric decompositions of aspherical 4-manifolds which fibre over 2-orbifolds. We show that no such manifold admits infinitely many fibrations over hyperbolic base orbifolds and that “most” Seifert fibred 4-manifolds over hyperbolic bases have a decomposition induced from a decomposition of

Geometric Decompositions of 4-dimensional Bundle Spaces

We consider geometric decompositions of aspherical 4manifolds which fibre over 2-orbifolds. We show first that no such manifold admits infinitely many fibrations over hyperbolic base orbifolds. If E is Seifert fibred over a hyperbolic surface B and either B has at most one cone point of order 2 or the monodromy has image in SL(2,Z) then E it has a decomposition induced from a decomposition of B...

Characteristic Classes of Bad Orbifold Vector Bundles

We show that every bad orbifold vector bundle can be realized as the restriction of a good orbifold vector bundle to a suborbifold of the base space. We give an explicit construction of this result in which the Chen-Ruan orbifold cohomology of the two base spaces are isomorphic (as additive groups). This construction is used to indicate an extension of the Chern-Weil construction of characteris...

Fourier Decompositions of Loop Bundles

In this paper we investigate bundles whose structure group is the loop group LU(n). These bundles are classified by maps to the loop space of the classifying space, LBU(n). Our main result is to give a necessary and sufficient criterion for there to exist a Fourier type decomposition of such a bundle ξ. This is essentially a decomposition of ξ as ζ⊗LC, where ζ is a finite dimensional subbundle ...

Representations of Orbifold Groups and Parabolic Bundles