2 problems

Goresky–MacPherson cellular deformation-retraction conjecture. There exists a $\nabla f$-like vector field $V$ on $X$ such that, with

In the situation of Theorem … k^-:{cal K}^-V(p)to{cal L}^-V(p),qquad k^+:{cal K}^+V(p)to{cal L}^+V(p), … h^-V(p):K^-V(p)to L^-V(p),qquad h^+V(p):K^+V(p)to L^+V(p). … , analogous to…