Introduction to orbifolds

Francisco C. Caramello Jr

Published 2019-09-18Version 1

In this survey we introduce orbifolds from the classical point of view. We relate orbifolds with group actions, we see how elementary objects from Algebraic Topology generalize to orbifolds, such as the fundamental group and Euler characteristic, then we proceed to the generalizations of classical objects from Differential Geometry to orbifolds, studding orbibundles, differential forms, integration and (equivariant) De Rham cohomology. Finally, we endow orbifolds with Riemannian metrics and survey some generalizations of classical results from Riemannian Geometry to this setting.