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Marek Kossowski - Characteristic classes for pseudo Riemannian manifolds with volume-resolvable metric singularities
MAREK KOSSOWSKI, Mathematics Department, University of South Carolina, Columbia, South Carolina 29208, USA | |
Characteristic classes for pseudo Riemannian manifolds with volume-resolvable metric singularities |
We consider compact orientied m-dimensional manifolds M, , with symmetric (0,2)-tensors which have maximal rank on an open dense subset, . The tensor will change bilinear type on a hypersurface , in a smooth transverse manner. The associated dual tensor will also change bilinear type on a hypersurface , in a smooth, transverse manner. The objective of this paper is to identify classes of for which the Chern-Weil construction adapts without residue. (We also examine the case of surfaces with ``corners'' where D0 and intersect transversally and a geometric residue naturally arises.) This is accomplished by way of the cannonical Volume blow up , i.e., the pullback metric will be ``less singular'' than . Moreover, the -manifolds ,provide a natural geometric setting for the resulting characteristics classes.
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