Characteristic Classes of Bad Orbifold Vector Bundles

Details Characteristic Classes of Bad Orbifold Vector Bundles Characteristic Classes of Bad Orbifold Vector Bundles

2006-06-27

arxiv.org/abs/math/0606665v2

Journal of Geometry and Physics 57 (2007), no. 11, 2365--2371

Mathematics

Differential Geometry

12 pages; improved exposition

Scientific paper

10.1016/j.geomphys.2007.08.001

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 characteristic classes to bad orbifold vector bundles. In particular, we apply this construction to the orbifold Euler class and demonstrate that it acts as an obstruction to the existence of nonvanishing sections.

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