Negatively curved bundles in the Igusa stable range
Farrell, Francis Thomas
Journal of Topology
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Bustamante, M., Farrell, F. T., & Jiang, Y. (2019). Negatively curved bundles in the Igusa stable range. Journal of Topology, 13 (1), 175-186. https://doi.org/10.1112/topo.12130
We use classical results in smoothing theory to extract information about the rational homotopy groups of the space of negatively curved metrics on a high dimensional manifold. It is also shown that smooth M-bundles over spheres equipped with fiberwise negatively curved metrics, represent elements of finite order in the homotopy groups of the classifying space for smooth M-bundles, provided the dimension of M is large enough.
The first author is supported by the DFG Priority Programme Geometry at Infinity (SPP 2026): Spaces and moduli spaces of Riemannian metrics with curvature bounds on compact and non‐compact manifolds. The third author is partially supported by the grant NSFC 11571343.
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External DOI: https://doi.org/10.1112/topo.12130
This record's URL: https://www.repository.cam.ac.uk/handle/1810/298130
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