A Poincaré index formula for surfaces with boundary (Q1979115)

From the authors summary: The authors give an easy extension of the Poincaré index formula from the disc to any smooth compact connected 2-dimensional manifold with boundary. In particular, they show that the sum of the indices of the vector field at the critical points depends only on the Euler characteristic of the surface and on the behaviour of its trajectories in the boundary. The theorem generalizes previous results of \textit{C. C. Pugh} [Topology 7, 217-226 (1968; Zbl 0194.24602)] and \textit{J. Llibre} and \textit{Ye Yanqian} [Bull. Soc. Math. de Belgique (to appear)].