2 problems

Let $(Y,\pi)$ be a fibred three-manifold, let $\operatorname{Sym}^n_{S^1}(Y)$ be its relative symmetric product, and let $\Omega\in\Omega^2(\operatorname{Sym}^n_{S^1}(Y))$ be a clo…

Let $(X,pi)$ be a broken fibration over a surface, with $I_pi\subset H_1(X;\Z)$ the subgroup of classes supported on a fibre, and let…