Topology of the configuration space of polygons as a codimension one submanifold of a torus (Q1974496)

By using Morse theory the authors obtain the topology of \[ \begin{aligned} W_{n+2,r}&= \{(w_1,\dots, w_n)\in T^n: |w_1+\cdots+ w_n+1|\geq r\}\\ \text{and} M_{n+2,r}&= \{(w_1,\dots, w_n)\in T^n: |w_1+\cdots+ w_n+1|= r\} \end{aligned} \] where \(T^n\) is the \(n\)-dimensional torus.