Homotopy types of diffeomorphism groups of polar Morse–Bott foliations on lens spaces, 2

Let F be a Morse–Bott foliation on the solid torus T = S 1 × D 2 into 2-tori parallel to the boundary and one singular central circle. Gluing two copies of T by some diffeomorphism between their boundaries, one gets a lens space L p , q with a Morse–Bott foliation F p , q obtained from F on each cop...

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Bibliographic Details
Published in:Journal of homotopy and related structures 2024-06, Vol.19 (2), p.239-273
Main Author: Maksymenko, Sergiy
Format: Article
Language:English
Subjects:
Algebra
Algebraic Topology
Functional Analysis
Isomorphism
Lenses
Mathematics
Mathematics and Statistics
Number Theory
Toruses
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Summary:Let F be a Morse–Bott foliation on the solid torus T = S 1 × D 2 into 2-tori parallel to the boundary and one singular central circle. Gluing two copies of T by some diffeomorphism between their boundaries, one gets a lens space L p , q with a Morse–Bott foliation F p , q obtained from F on each copy of T and thus consisting of two singular circles and parallel 2-tori. In the previous paper Khokliuk and Maksymenko (J Homotopy Relat Struct 18:313–356. https://doi.org/10.1007/s40062-023-00328-z , 2024) there were computed weak homotopy types of the groups D lp ( F p , q ) of leaf preserving (i.e. leaving invariant each leaf) diffeomorphisms of such foliations. In the present paper it is shown that the inclusion of these groups into the corresponding group D + fol ( F p , q ) of foliated (i.e. sending leaves to leaves) diffeomorphisms which do not interchange singular circles are homotopy equivalences.
ISSN:2193-8407
1512-2891
DOI:10.1007/s40062-024-00346-5