This chapter provides the Eisenstein cohomology. It begins with the Poincaré duality and maximal isotropic subspace of boundary cohomology. Here, the chapter considers the compatibility of duality isomorphisms with the connecting homomorphism. It then states and proves the main result on rank-one Eisenstein cohomology. Thereafter, the chapter presents a theorem of Langlands: the constant term of an Eisenstein series. It draws some details from the Langlands–Shahidi method in this context. Induced representations are examined, as are standard intertwining operators. The chapter finally illustrates the Eisenstein series, the constant term of an Eisenstein series, and the holomorphy of the Eisenstein series at the point of evaluation.
Keywords: Eisenstein cohomology, boundary cohomology, Poincaré duality, duality isomorphisms, connecting homomorphism, Langlands–Shahidi method, induced representations, standard intertwining operators, Eisenstein series
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