Cayley fibrations in the Bryant–Salamon Spin(7) manifold

On each complete asymptotically conical Spin ( 7 ) manifold constructed by Bryant and Salamon, including the asymptotic cone, we consider a natural family of SU ( 2 ) actions preserving the Cayley form. For each element of this family, we study the (possibly singular) invariant Cayley fibration, whi...

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Bibliographic Details
Published in:Annali di matematica pura ed applicata 2023-06, Vol.202 (3), p.1131-1171
Main Author: Trinca, Federico
Format: Article
Language:English
Subjects:
Asymptotic properties
Manifolds (mathematics)
Mathematics
Mathematics and Statistics
Topology
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Summary:On each complete asymptotically conical Spin ( 7 ) manifold constructed by Bryant and Salamon, including the asymptotic cone, we consider a natural family of SU ( 2 ) actions preserving the Cayley form. For each element of this family, we study the (possibly singular) invariant Cayley fibration, which we describe explicitly, if possible. These can be reckoned as generalizations of the trivial flat fibration of R 8 and the product of a line with the Harvey–Lawson coassociative fibration of R 7 . The fibres will provide new examples of asymptotically conical Cayley submanifolds in the Bryant–Salamon manifolds of topology R 4 , R × S 3 and O C P 1 ( - 1 ) .
ISSN:0373-3114
1618-1891
DOI:10.1007/s10231-022-01273-z