XXXII Workshop on Geometric Methods in Physics 30.06-6.07.2013

Alexander Schmeding

Diffeomorphism groups of non-compact orbifolds

Orbifolds are a generalization of manifolds. They arise naturally in different areas of mathematics and physics, e.g.:
- Spaces of symplectic reduction are orbifolds,
- Orbifolds may be used to construct a conformal field theory model (cf. [1]),

We consider the diffeomorphism group of a paracompact, non-compact smooth
reduced orbifold. Our main result is the construction of an infinite
dimensional Lie-group structure on the diffeomorphism group and several interesting subgroups (our exposition follows [3]). Here orbifold morphisms are understood as maps in the sense of [2]. In the talk we sketch the construction and its main ingredients.

[1] Dixon, L.J., Harvey, J.A., Vafa, C. and Witten, E.: Strings on orbifolds. I, Nuclear Phys. B 261:4 (1985), 678-686
[2] Pohl, A.D.: Convenient categories of reduced orbifolds arXiv:1001.0668v4 [math.GT], January 2010,
[3] Schmeding, A.: The diffeomorphism group of a non-compact orbifold arXiv:1301.5551 [math.GR], January 2013,

Event sponsored by:
Belgian Science Policy Office     PAI          University
of Bialystok
University of Bialystok

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