Rationality of geometric signatures of complete 4-manifolds |
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Authors: | Rong Xiaochun |
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Institution: | (1) Mathematics Department, Columbia University, 10027 New York, NY, USA;(2) Present address: Mathematics Department, University of Chicago, 60637 Chicago, IL, USA |
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Abstract: | Summary According to CG4]|and CFG], the complete manifolds with bounded sectional curvature and finite volume admit positive rank F-structures near infinity. In this paper, we show that, in dimension four, if the manifolds also have bounded covering geometry near infinity, then there exist F-structures with special topological properties. F-structures with these properties cannot be constructed solely by means of the general methods in CG4]|and CFG]. Using these special properties we prove a conjecture of Cheeger-Gromov on the rationality of the geometric signatures in the four dimensional case.Oblatum 15-XI-1993This work was partially supported by NSF Grant NSF DMS 9204095. |
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