All Questions

To start with, consider some abstract $3$-dimensional simplicial complex $\Delta$ representing a manifold without boundary, for simplicity. Then, there is this well-known construction of the "(...

A friend of mine recently asked me if I knew any simple, conceptual argument (even one that is perhaps only heuristic) to show that if a triangulated manifold has a non-vanishing vector field, then ...

One of the corollaries of the Poincaré–Hopf index theorem is that a closed, connected manifold $M$ admits non-vanishing vector fields iff its Euler characteristic is zero; i.e. $\chi(M) = 0$. I am ...