Sphere fibrations over highly connected manifolds

Article Type

Research Article

Publication Title

Journal of the London Mathematical Society

Abstract

We construct sphere fibrations over (Formula presented.) -connected (Formula presented.) -manifolds such that the total space is a connected sum of sphere products. More precisely, for (Formula presented.) even, we construct fibrations (Formula presented.), where (Formula presented.) is a (Formula presented.) -connected (Formula presented.) -dimensional Poincaré duality complex that satisfies (Formula presented.), in a localised category of spaces. The construction of the fibration is proved for (Formula presented.), where the prime 2, and the primes that occur as torsion in (Formula presented.) are inverted. In specific cases, by either assuming (Formula presented.) is small, or assuming (Formula presented.) is large we can reduce the number of primes that need to be inverted. Integral results are obtained for (Formula presented.) or 4, and if (Formula presented.) is bigger than the number of cyclic summands in the stable stem (Formula presented.), we obtain results after inverting 2. Finally, we prove some applications for fibrations over (Formula presented.), and for looped configuration spaces.

DOI

10.1112/jlms.70002

Publication Date

11-1-2024

Comments

Open Access; Green Open Access

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