Marek Kossowski - Characteristic classes for pseudo Riemannian manifolds with volume-resolvable metric singularities

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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 $C^\infty$ compact orientied m-dimensional manifolds M, $\partial M =\sigma$ , with symmetric (0,2)-tensors $\langle\,,\,\rangle$ which have maximal rank on an open dense subset, $M-(D^0 \cup D^\infty)$ . The tensor $\langle\,,\,\rangle$ will change bilinear type on a hypersurface $D^0 \subset M$ , in a smooth transverse manner. The associated dual tensor ${}^\ast \langle\, ,\,\rangle$ will also change bilinear type on a hypersurface $D^\infty\subset M$ , in a smooth, transverse manner. The objective of this paper is to identify classes of $(M, \langle\,,\,\rangle)$ for which the Chern-Weil construction adapts without residue. (We also examine the case of surfaces with ``corners'' where D⁰ and $D^\infty$ intersect transversally and a geometric residue naturally arises.) This is accomplished by way of the cannonical Volume blow up $\rho\colon \textrm{VB}^\pm\rightarrow M - (D^0 \cup D^\infty)$ , i.e., the pullback metric $\rho^\ast \langle\,,\,\rangle$ will be ``less singular'' than $\langle\,,\,\rangle$ . Moreover, the $C^\infty$ -manifolds $\textrm{VB}^\pm$ ,provide a natural geometric setting for the resulting characteristics classes.

Next: Hans-Peter Künzle - -Einstein-Yang-Mills Up: Relativity and Geometry / Previous: Conrad Hewitt - Three

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