In differential geometry, the Euler characteristic of an orbifold, or orbifold Euler characteristic, is a generalization of the topological Euler characteristic that includes contributions coming from nontrivial automorphisms.
In particular, unlike a topological Euler characteristic, it is not restricted to integer values and is in general a rational number.
It is of interest in mathematical physics, specifically in string theory.
quotiented by a finite group
, the sum runs over all pairs of commuting elements of
is the space of simultaneous fixed points of
in the summation is the usual Euler characteristic.
)[1][2] If the action is free, the sum has only a single term, and so this expression reduces to the topological Euler characteristic of
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