Global stable splittings of Stiefel manifolds
Stefan SchwedeMathematisches Institut, Universität Bonn, 53115 Bonn, Germany
We prove global equivariant refinements of Miller's stable splittings of the infinite orthogonal, unitary and symplectic groups, and more generally of the spaces and . As such, our results encode compatible equivariant stable splittings, for all compact Lie groups, of specific equivariant refinements of these spaces.
In the unitary and symplectic case, we also take the actions of the Galois groups into account. To properly formulate these Galois-global statements, we introduce a generalization of global stable homotopy theory in the presence of an extrinsic action of an additional topological group.
Cite this article
Stefan Schwede, Global stable splittings of Stiefel manifolds. Doc. Math. 27 (2022), pp. 789–845DOI 10.4171/DM/885