A Complete Obstruction to the Existence of Nonvanishing Vector Fields on Almost-Complex, Closed, Cyclic Orbifolds

Abstract

We determine several necessary and sufficient conditions for a closed almost-complex orbifold $Q$ with cyclic local groups to admit a nonvanishing vector field. These conditions are stated separately in terms of the orbifold Euler-Satake characteristics of $Q$ and its sectors, the Euler characteristics of the underlying topological spaces of $Q$ and its sectors, and in terms of the orbifold Euler class $e_{orb}(Q)$ in Chen-Ruan orbifold cohomology $H_{orb}^{\ast }(Q;\mathbb{R})$.

11 pages v3: added more exposition and additional proofs, added hypothesis of cyclic

Cited by in corpus (1)

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