The cohomology $H ^* (\Gamma, E)$ of an arithmetic subgroup
$\Gamma$ of a connected reductive algebraic group $G$ defined over
some algebraic number field $F$ can be interpreted in terms of the
automorphic spectrum of $\Gamma$. With this framework in place,
there is a sum decomposition of the cohomology into the cuspidal
cohomology (i.e., classes represented by cuspidal automorphic
forms for $G$) and the so-called Eisenstein cohomology constructed
as the span of appropriate residues or derivatives of Eisenstein
series attached to cuspidal automorphic forms on the Levi
components of proper parabolic $F$-subgroups of $G$. The main
objective of this paper is to isolate a specific structural part
in the Eisenstein cohomology. This pertains to regular Eisenstein
cohomology classes attached to cuspidal automorphic
representations whose archimedean component is tempered. It is
shown that the cohomological degree of these classes is bounded
from below by the constant $q_0(G(\mathbb{R}))=((1/2) [\dim
X_{G(\mathbb{R})}-(\rk (G(\mathbb{R}))-\rk(K_{\mathbb{R}}))]$,
where $K_{\mathbb{R}}$ denotes a maximal compact subgroup of the
real Lie group $G(\mathbb{R})$, where $X_{G(\mathbb{R})}$ is the
associated symmetric space. This investigation has various
applications. One of these is a vanishing result for the
cohomology in the generic case (i.e., where the representation
determining the coefficient system $E$ has regular highest weight)
in degrees below $q_0(G(\mathbb{R}))$. This is a sharp bound
depending only on the underlying real Lie group $G(\mathbb{R})$
(Corollary 5.6, Proposition 5.8). This result is supplemented by a
qualitative structural result in the description of the cohomology
in higher degrees by means of regular Eisenstein cohomology
classes.