A generalized Reeb component is a pair 
consisting of a compact
manifold 
with nonempty boundary and a transversely
orientable codimension-one foliation 
on 
which is tangent to 
, such that the foliation holonomy groups of all leaves
in the interior 
are trivial, all interior leaves are noncompact, and all leaves
of 
are proper. Generalized Reeb components are obvious generalizations of Reeb
components.
The introduction of the generalized version of the Reeb component facilitates the proof of many significant
results in the theory of 3-manifolds and of foliations.
It is well-known that generalized Reeb components are transversely
orientable and that a manifold 
admitting a generalized Reeb component also admits a nice
vector field 
(Imanishi and Yagi 1976). Moreover, given a generalized Reeb
component 
,
is a fibration over 
.
Like many notions in geometric topology, the generalized Reeb component can be presented in various contexts. One source describes a generalized
Reeb component on a closed manifold of dimension
3 
with foliation 
to be a submanifold 
of maximal dimension
which is bounded by tori 
such that the orientation
of these tori as leaves of 
is the same as (or simultaneously opposite to) their orientation
as the boundary components of 
(Eliashberg and Thurston 1998). Framed in this way, generalized
Reeb components are shown to have deep connections to various notions in foliation
theory, e.g., in presenting an existence criterion for a closed 3-manifold 
to admit a taut foliation.
