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 eorb(Q) in Chen-Ruan orbifold cohomology Horb (Q; ).
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.