Smooth functions that split a Klein bottle into two Möbius bands

Bohdan Mazhar, Sergiy Maksymenko

Given a compact surface $M$, consider the right action ${\mathcal{C}}^{\infty }(M)\times \mathcal{D}(M)\to {\mathcal{C}}^{\infty }(M)$, $(f,h)\mapsto f\circ h$, of the group $\mathcal{D}…