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arXiv · 0902.2220

Classifying closed 2-orbifolds with Euler characteristics

Whitney DuVal·John Schulte·Christopher Seaton·Bradford Taylor
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Abstract

We determine the extent to which the collection of $Γ$-Euler-Satake characteristics classify closed 2-orbifolds. In particular, we show that the closed, connected, effective, orientable 2-orbifolds are classified by the collection of $Γ$-Euler-Satake characteristics corresponding to free or free abelian $Γ$ and are not classified by those corresponding to any finite collection of finitely generated discrete groups. Similarly, we show that such a classification is not possible for non-orientable 2-orbifolds and any collection of $Γ$, nor for noneffective 2-orbifolds. As a corollary, we generate families of orbifolds with the same $Γ$-Euler-Satake characteristics in arbitrary dimensions for any finite collection of $Γ$; this is used to demonstrate that the $Γ$-Euler-Satake characteristics each constitute new invariants of orbifolds.

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Whitney DuVal, John Schulte, Christopher Seaton, Bradford Taylor. 2009-02-12. Classifying closed 2-orbifolds with Euler characteristics. https://doi.org/10.1017/s001708951000042x

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