Since the seminal work of Chen and Ruan [1, 2, and 3] there has been a renaissance in the mathematical study of the geometry and topology of orbifolds, but this time the road has been informed by mathematical-physics, and in particular by string theory. This has also allowed a clarification of the old concepts and definitions [4, 5, and 6]. These lectures are thus devoted to the recent developments in this area of rapid growth.
We will talk about orbifolds, their cohomology theories, twistings of these theories (gerbes), and their interactions with mathematical-physics.
What is an orbifold?
Orbifold Cohomology Theories
Gerbes over Orbifold
The McKay-Ruan correspondences
The looporbifold
[1] Chen, Weimin; Ruan, Yongbin. A new cohomology theory of orbifold. Comm. Math. Phys. 248 (2004), no. 1, 1--31.
[2] Ruan, Yongbin. Stringy orbifolds. Orbifolds in mathematics and physics (Madison, WI, 2001), 259--299, Contemp. Math., 310, Amer. Math. Soc., Providence, RI, 2002.
[3] Chen, Weimin; Ruan, Yongbin. Orbifold Gromov-Witten theory. Orbifolds in mathematics and physics (Madison, WI, 2001), 25--85, Contemp. Math., 310, Amer. Math. Soc., Providence, RI, 2002.
A localization principle for orbifold theories
Updated 14/09/2005