216,760 research outputs found
In search of an appropriate abstraction level for motif annotations
In: Proceedings of the 2012 Workshop on Computational Models of Narrative, (pp. 22-28).
Morse Inequalities for Orbifold Cohomology
This paper begins the study of Morse theory for orbifolds, or more precisely
for differentiable Deligne-Mumford stacks. The main result is an analogue of
the Morse inequalities that relates the orbifold Betti numbers of an
almost-complex orbifold to the critical points of a Morse function on the
orbifold. We also show that a generic function on an orbifold is Morse. In
obtaining these results we develop for differentiable Deligne-Mumford stacks
those tools of differential geometry and topology -- flows of vector fields,
the strong topology -- that are essential to the development of Morse theory on
manifolds
- …