Vector Fields on Manifolds
- 147 Downloads
This paper is a contribution to the topological study of vector fields on manifolds. In particular we shall be concerned with the problems of existence of r linearly independent vector fields. For r = 1 the classical result of H. Hopf asserts that the vanishing of the Euler characteristic is the necessary and sufficient condition, and our results will give partial extensions of Hopfs theorem to the case r > 1. A recent article by E. Thomas  gives a good survey of work in this general area.
Unable to display preview. Download preview PDF.
Topology of Elliptic Operators
- M. F. Atiyah, Amer. Math. Symposium on Global Analysis (Berkeley, 1968).Google Scholar
- The index of elliptic operators: III, Ann. of Math. 87 (1968), 546–604.Google Scholar
- Index theory for skew-adjoint Fredholm operators, Publ. Math. I.H.E.S. (1970) (to appear).Google Scholar
- D. Frank (to appear).Google Scholar