ORBIFOLDS AND STRINGY TOPOLOGY

By WILLIAM JONES

CONTENTS FOUNDATIONS CLASSICAL EFFECTIVE ORBIFOLDS EXAMPLES COMPARING ORBIFOLDS TO MANIFOLDS GROUPOIDS ORBIFOLDS AS SINGULAR SPACES COHOMOLOGY, BUNDLES AND MORPHISMS DE RHAM AND SINGULAR COHOMOLOGY OF ORBIFOLDS THE ORBIFOLD FUNDAMENTAL GROUP AND COVERING SPACES ORBIFOLD VECTOR BUNDLES AND PRINCIPAL BUNDLES ORBIFOLD MORPHISMS CLASSI?CATION OF ORBIFOLD MORPHISMS ORBIFOLD K-THEORY INTRODUCTION ORBIFOLDS, GROUP ACTIONS, AND BREDON COHOMOLOGY ORBIFOLD BUNDLES AND EQUIVARIANT K-THEORY A DECOMPOSITION FOR ORBIFOLD K-THEORY PROJECTIVE REPRESENTATIONS, TWISTED GROUP ALGEBRAS, AND EXTENSIONS TWISTED EQUIVARIANT K-THEORY TWISTED ORBIFOLD K-THEORY AND TWISTED BREDON COHOMOLOGY CHEN–RUAN COHOMOLOGY TWISTED SECTORS DEGREE SHIFTING AND POINCAR´E PAIRING CUP PRODUCT SOME ELEMENTARY EXAMPLES CHEN–RUAN COHOMOLOGY TWISTED BY A DISCRETE TORSION CALCULATING CHEN–RUAN COHOMOLOGY ABELIAN ORBIFOLDS SYMMETRIC PRODUCTS