论文标题
在9个manifolds上的接触结构的存在
The existence of contact structures on 9-manifolds
论文作者
论文摘要
我们为封闭的9型manifold M提供了必要和足够的条件，以便接触几乎接触结构。根据M的Stiefel-Whitney类和M.其他更微妙的同型不变性，这些条件是根据M. 在Borman，Eliashberg和Murphy的基本结果下，M在且仅当M承认过度扭曲的接触结构时，几乎承认了接触结构。因此，我们给出了M的必要条件，以使M接触过度扭转的接触结构，并且我们证明，如果N是另一个封闭的9个manifold，那是同等的，则与M相等，则M在且仅在N时承认过度扭转的接触结构。 此外，对于W_i（M）M的I-The Intemall-Stiefel-Whitney类，我们证明，如果W_3（M）= 0，则W_7（M）= 0。
We give necessary and sufficient conditions for a closed orientable 9-manifold M to admit an almost contact structure. The conditions are stated in terms of the Stiefel-Whitney classes of M and other more subtle homotopy invariants of M. By a fundamental result of Borman, Eliashberg and Murphy, M admits an almost contact structure if and only if M admits an over-twisted contact structure. Hence we give necessary and sufficient conditions for M to admit an over-twisted contact structure and we prove that if N is another closed 9-manifold which is homotopy equivalent to M, then M admits an over-twisted contact structure if and only if N does. In addition, for W_i(M) the i-th integral Stiefel-Whitney class of M, we prove that if W_3(M) = 0 then W_7(M) = 0.
