Orbifolds and Stringy Topology Book

Introduction     vii
Foundations     1
Classical effective orbifolds     1
Examples     5
Comparing orbifolds to manifolds     10
Groupoids     15
Orbifolds as singular spaces     28
Cohomology, bundles and morphisms     32
De Rham and singular cohomology of orbifolds     32
The orbifold fundamental group and covering spaces     39
Orbifold vector bundles and principal bundles     44
Orbifold morphisms     47
Classification of orbifold morphisms     50
Orbifold K-theory     56
Introduction     56
Orbifolds, group actions, and Bredon cohomology     57
Orbifold bundles and equivariant K-theory     60
A decomposition for orbifold K-theory     63
Projective representations, twisted group algebras, and extensions     69
Twisted equivariant K-theory     72
Twisted orbifold K-theory and twisted Bredon cohomology     76
Chen-Ruan cohomology     78
Twisted sectors     80
Degree shifting and Poincare pairing     84
Cup product     88
Some elementary examples     95
Chen-Ruancohomology twisted by a discrete torsion     98
Calculating Chen-Ruan cohomology     105
Abelian orbifolds     105
Symmetric products     115
References     138
Index     146