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- W4317940181 abstract "Given a smooth action of the sphere $mathbb S^3$ on a manifold $M$, we have previously constructed a Gysin sequence relating the cohomology of the manifold $M$ and that of the orbit space $M/mathbb S^3$. This sequence involves an exotic term depending on the subset $M^{mathbb S^1}$. Notice that the orbit space is a stratified pseudomanifold, a kind of singular spaces where intersection cohomology applies. In the case where the the action is semi-free, the first author has already constructed a Gysin sequence relating the cohomology of $M$ and the intersection cohomology of $M/mathbb S^3$. What happens if the action is not semi-free? This is the goal of this work. The situation is more complicated and we do not find a Gysin sequence but a Gysin braid relating the cohomology of $M$ and the intersection cohomology of $M/mathbb S^3$. This braid also contains an exotic term depending this time on the intersection cohomology of $M^{mathbb S^1}$." @default.
- W4317940181 created "2023-01-25" @default.
- W4317940181 creator A5076732387 @default.
- W4317940181 creator A5082006756 @default.
- W4317940181 date "2023-01-21" @default.
- W4317940181 modified "2023-10-07" @default.
- W4317940181 title "The Gysin braid for $S^3$-actions on manifolds" @default.
- W4317940181 doi "https://doi.org/10.48550/arxiv.2301.09002" @default.
- W4317940181 hasPublicationYear "2023" @default.
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