科研之友
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摘要
We introduce a complete obstruction to the existence of nonvanishing vector fields on a closed orbifold Q. Motivated by the inertia orbifold, the space of multi-sectors, and the generalized orbifold Euler characteristics, we construct for each finitely generated group P an orbifold called the space of Gamma-sectors of Q. The obstruction Occurs as the Euler-Satake characteristics of the Gamma-sectors for an appropriate choice of Gamma; in the case that Q is oriented, this obstruction is expressed as a cohomology class, the Gamma-Euler-Satake class. We also acquire a complete obstruction in the case that Q is compact with boundary and in the case that Q is an open suborbifold of a closed orbifold.
- 出版日期2010-1
