On negatively curved bundles with hyperbolic fibers outside the Igusa stable range

Bustamante, Mauricio; Farrell, F. T.; Jiang, Yi

doi:10.1007/s00208-018-1691-y

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2020

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“…Nonetheless elements of infinite order in

π_{i} {scriptT}^{< 0} false(M false)

can be obtained if we look outside Igusa's stable range. We elaborate on this in .…”

Section: Introductionmentioning

confidence: 99%

Negatively curved bundles in the Igusa stable range

Bustamante

Farrell

Jiang

2020

Journal of Topology

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We use classical results in smoothing theory to extract information about the rational homotopy groups of the space of Riemannian metrics without conjugate points on a high‐dimensional manifold with hyperbolic fundamental group. As a consequence, we show that spaces of negatively curved Riemannian metrics have in general nontrivial rational homotopy groups. We also show that smooth M‐bundles over spheres equipped with fiberwise negatively curved metrics represent elements of finite order in the homotopy groups πiBDifffalse(Mfalse) of the classifying space for smooth M‐bundles, provided i≪dimM.

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“…Nonetheless elements of infinite order in