The volume of a differentiable stack

Details The volume of a differentiable stack The volume of a differentiable stack

2008-09-12

arxiv.org/abs/0809.2130v3

Mathematics

Differential Geometry

20 pages, To appear in proceedings of Poisson 2008 (Lausanne, July 2008), further minor revisions

Scientific paper

We extend the notion of the cardinality of a discrete groupoid (equal to the Euler characteristic of the corresponding discrete orbifold) to the setting of Lie groupoids. Since this quantity is an invariant under equivalence of groupoids, we call it the volume of the associated stack rather than of the groupoid itself. Since there is no natural measure in the smooth case like the counting measure in the discrete case, we need extra data to define the volume. This data has the form of an invariant section of a natural line bundle over the groupoid. Sections of a square root of this line bundle constitute an "intrinsic Hilbert space" of the stack.

Affiliated with

Also associated with

No associations

Rating

The volume of a differentiable stack does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The volume of a differentiable stack, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The volume of a differentiable stack will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-368684