Boundary Cohomology
Boundary Cohomology
This chapter discusses some relevant details of the cohomology of the boundary of the Borel–Serre compactification of the locally symmetric space SGKf. It first illustrates a spectral sequence converging to boundary cohomology. The chapter then turns to the cohomology of ∂PSG to better understand the cohomology of the boundary. Finally, the chapter describes the contribution of the discrete but noncuspidal spectrum to cohomology. It formulates the consequences of the description of the discrete spectrum in Mœglin–Waldspurger for the square integrable cohomology. In a sense, the chapter makes their results more explicit. It works at a transcendental level: the coefficient systems are ℂ-vector spaces.
Keywords: boundary cohomology, Borel–Serre compactification, locally symmetric space, discrete spectrum, Mœglin–Waldspurger, square integrable cohomology
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