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- W3122122108 abstract "$Gamma$-structures are weak forms of multiplications on closed oriented manifolds. As shown by Hopf the rational cohomology algebras of manifolds admitting $Gamma$-structures are free over odd degree generators. We prove that this condition is also sufficient for the existence of $Gamma$-structures on manifolds which are nilpotent in the sense of homotopy theory. This includes homogeneous spaces with connected isotropy groups. Passing to a more geometric perspective we show that on compact oriented Riemannian symmetric spaces with connected isotropy groups and free rational cohomology algebras the canonical products given by geodesic symmetries define $Gamma$-structures. This extends work of Albers, Frauenfelder and Solomon on $Gamma$-structures on Lagrangian Grassmannians." @default.
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- W3122122108 date "2018-03-12" @default.
- W3122122108 modified "2023-10-16" @default.
- W3122122108 title "Γ–structures and symmetric spaces" @default.
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- W3122122108 doi "https://doi.org/10.2140/agt.2018.18.877" @default.
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