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We introduce a ''folded sum operation'' which glues two compact mapping torialong their common (diffeomorphic) boundaries. We call the resulting closedmanifold a ''folded sum of mapping tori'', and it naturally fibers over thecircle. We show that any folded sum $M$ of two ''contact'' mapping tori (theirfibers are compact exact symplectic manifolds with contactomorphic convexboundaries) admits a cooriented contact structure which is ''compatible'' (in acertain sense) with the resulting fibration map from $M$ onto the circle.Moreover, we study the tightness of the resulting contact structure on $M$ forcertain cases. This gives a new method of constructing closed contact manifoldsin any odd dimension. In particular, it recovers some earlier constructions andresults. More interestingly, in dimension three, it provides the existence oftight contact structures on a large class of (hyperbolic) surface bundles overthe circle.

Contact Structures on Folded Sums of Contact Mapping Tori and Surface Bundles