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- W4385659213 abstract "Let $$T= S^1times D^2$$ be the solid torus, $$mathcal {F}$$ the Morse–Bott foliation on T into 2-tori parallel to the boundary and one singular circle $$S^1times 0$$ , which is the central circle of the torus T, and $$mathcal {D}(mathcal {F},partial T)$$ the group of diffeomorphisms of T fixed on $$partial T$$ and leaving each leaf of the foliation $$mathcal {F}$$ invariant. We prove that $$mathcal {D}(mathcal {F},partial T)$$ is contractible. Gluing two copies of T by some diffeomorphism between their boundaries, we will get a lens space $$L_{p,q}$$ with a Morse–Bott foliation $$mathcal {F}_{p,q}$$ obtained from $$mathcal {F}$$ on each copy of T. We also compute the homotopy type of the group $$mathcal {D}(mathcal {F}_{p,q})$$ of diffeomorphisms of $$L_{p,q}$$ leaving invariant each leaf of $$mathcal {F}_{p,q}$$ ." @default.
- W4385659213 created "2023-08-09" @default.
- W4385659213 creator A5047222685 @default.
- W4385659213 creator A5065452579 @default.
- W4385659213 date "2023-08-08" @default.
- W4385659213 modified "2023-09-27" @default.
- W4385659213 title "Homotopy types of diffeomorphism groups of polar Morse–Bott foliations on lens spaces, 1" @default.
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- W4385659213 doi "https://doi.org/10.1007/s40062-023-00328-z" @default.
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