Geodesic
Global stable splittings of Stiefel manifolds
Documenta mathematica, Tome 27 (2022), pp. 789-845.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

We prove global equivariant refinements of Miller's stable splittings of the infinite orthogonal, unitary and symplectic groups, and more generally of the spaces $O/O(m), U/U(m)$ and $Sp/Sp(m)$. As such, our results encode compatible equivariant stable splittings, for all compact Lie groups, of specific equivariant refinements of these spaces. \par 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.
Classification : 55N91, 55P91
Keywords: global homotopy theory, stable splitting, Stiefel manifold 
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     author = {Schwede, Stefan},
     title = {Global stable splittings of {Stiefel} manifolds},
     journal = {Documenta mathematica},
     pages = {789--845},
     publisher = {mathdoc},
     volume = {27},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2022__27__a46/}
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Schwede, Stefan. Global stable splittings of Stiefel manifolds. Documenta mathematica, Tome 27 (2022), pp. 789-845. http://geodesic.mathdoc.fr/item/DOCMA_2022__27__a46/