2021
DOI: 10.48550/arxiv.2106.02379
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Global stable splittings of Stiefel manifolds

Abstract: 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.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 generali… Show more

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Cited by 2 publications
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“…There, various model structures were given for a discrete group G not necessarily finite. Orthogonal spaces and orthogonal spectra with a G-action for a compact Lie group G were also studied from the global point of view in [Sch21], however no model structure was defined there.…”
Section: Introductionmentioning
confidence: 99%
“…There, various model structures were given for a discrete group G not necessarily finite. Orthogonal spaces and orthogonal spectra with a G-action for a compact Lie group G were also studied from the global point of view in [Sch21], however no model structure was defined there.…”
Section: Introductionmentioning
confidence: 99%
“…the study of global infinite loop spaces [Len20a,Chapter 2] or in the form of various 'Galois-global' phenomena [Sch21].…”
Section: Introductionmentioning
confidence: 99%