Astérisque 2012; 169 pp; softcover Number: 343 ISBN10: 2856293425 ISBN13: 9782856293423 List Price: US$60 Member Price: US$48 Order Code: AST/343
 The authors establish the general machinery of string topology for differentiable stacks. This machinery allows them to treat on equal footing free loops in stacks and hidden loops. They construct a bivariant (in the sense of Fulton and MacPherson) theory for topological stacks: it gives them a flexible theory of Gysin maps, which are automatically compatible with pullback, pushforward and products. Then the authors prove an excess formula in this context. The authors introduce oriented stacks, generalizing oriented manifolds, which are stacks on which they can do string topology. They prove that the homology of the free loop stack of an oriented stack and the homology of hidden loops (sometimes called ghost loops) are Frobenius algebras which are related by a natural morphism of Frobenius algebras. They also prove that the homology of the free loop stack has a natural structure of \(BV\)algebra which, together with the Frobenius structure, fits into homological conformal field theories with closed positive boundaries. They also use their constructions to study an analogue of the loop product for stacks of maps of (\(n\)dimensional) spheres to oriented stacks and compatible power maps in their homology. Using their general machinery, the authors construct an intersection pairing for (not necessarily compact) almost complex orbifolds which is in the same relation to the intersection pairing for manifolds as ChenRuan orbifold cupproduct is to ordinary cupproduct of manifolds. They show that the hidden product of almost complex orbifolds is isomorphic to the orbifold intersection pairing twisted by a canonical class. Finally they gave some examples, including the case of the classifying stacks \([*/G]\) of a compact Lie group. A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list. Readership Graduate students and research mathematicians interested in string topology, topological stacks, and loop stacks. Table of Contents  Topological stacks
 Homotopy type of a topological stack
 Vector bundles on stacks
 Thom isomorphism
 Loop stacks
 Bounded proper morphisms of topological stacks
 Bivariant theory for topological stacks
 Regular embeddings, submersions, and normally nonsingular morphisms
 Gysin maps
 The loop product
 Hidden loop product for family of groups over a stack
 Frobenius algebra structures
 The \(BV\)algebra on the homology of free loop stack
 Homological conformal field theory and free loop stacks
 Remarks on brane topology for stacks
 Orbifold intersection pairing
 Examples
 Bibliography
