Sphere fibrations over highly connected manifolds

We construct sphere fibrations over $(n-1)$-connected $2n$-manifolds such that the total space is a connected sum of sphere products. More precisely, for $n$ even, we construct fibrations $S^{n-1}\to {\mathrm{\#}}^{k-1}(S^n\times S^{2n-1})\to M_k$, where $M_k$ is a $(n-1)$-connected $2n$-dimensional Poincaré duality complex which satisfies $H_n(M_k)\cong {\mathbb{Z}}^k$, in a localized category of spaces. The construction of the fibration is proved for $k\ge 2$, where the prime $2$, and the primes which occur as torsion in ${\pi }_{2n-1}(S^n)$ are inverted. In specific cases, by either assuming $n$ is small, or assuming $k$ is large we can reduce the number of primes that need to be inverted. Integral results are obtained for $n=2$ or $4$, and if $k$ is bigger than the number of cyclic summands in the stable stem ${\pi }_{n-1}^s$, we obtain results after inverting $2$. Finally, we prove some applications for fibrations over $N\mathrm{\#}{M}_k$, and for looped configuration spaces.