For d≥6 and every k≥1, a new rational decomposition of spaces of homeomorphisms yields R^d-bundles over S^{4k} with nonzero kth rational Pontryagin class, plus a rational section of the stabilization map.
Boavida de Brito and G
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Pontryagin-Weiss classes and a rational decomposition of spaces of homeomorphisms
For d≥6 and every k≥1, a new rational decomposition of spaces of homeomorphisms yields R^d-bundles over S^{4k} with nonzero kth rational Pontryagin class, plus a rational section of the stabilization map.