Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I've heard people talk about the Euler characteristic of a stack, and I understand that it is sometimes fractional. This tells me that it is not defined in any usual sense like $\sum (-1)^i\dim H^i(X)$. What is the definition? What are good references for this? What is the inspiration for the definition?

share|cite|improve this question
Stacks are closely related to orbifolds, and orbifolds have a definition of Euler characteristic. I think one of the key motivations for orbifold Euler characteristic is that it should be multiplicative under finite covering spaces. – Ryan Budney Aug 31 '11 at 3:30

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.