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

Christopher Seaton

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

Differential Geometry 2007-05-23 v3

Authors: Christopher Seaton

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 $H_{orb}^\ast (Q; \R)$ .

Keywords

almost-complex orbifolds nonvanishing vector fields cyclic local groups orbifold euler-satake characteristic chen-ruan orbifold cohomology

Cite

@article{arxiv.math/0408187,
  title  = {A Complete Obstruction to the Existence of Nonvanishing Vector Fields on Almost-Complex, Closed, Cyclic Orbifolds},
  author = {Christopher Seaton},
  journal= {arXiv preprint arXiv:math/0408187},
  year   = {2007}
}

Comments

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

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

Abstract

Keywords

Cite

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