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Decompositions into codimension-two manifolds. (English) Zbl 0568.57013
This paper establishes the result that the decomposition space of a usc decomposition of an orientable $$(n+2)$$-manifold into continua having the shape of closed orientable n-manifolds is itself a 2-manifold.
From the introduction: ”This theorem lifts what is known about decompositions into codimension-two submanifolds to nearly the same level as what is known about decompositions into codimension-one submanifolds.” In particular, this paper extends work by Liem and by Daverman on codimension-one decompositions and a previous joint paper by the same authors [Topology Appl. 19, 103-121 (1985)]. They state that the present work evolved from techniques of their previous paper, ”which were inspired for the most part by methods of Coram and Duvall”.
Finally, the authors point out that the relatively nice results for decompositions into codimension-one or -two submanifolds ”do not persist through successively larger codimensions”. For codimension three, the decomposition space need not even be a generalized manifold.
Reviewer: L.Cannon

##### MSC:
 57N15 Topology of the Euclidean $$n$$-space, $$n$$-manifolds ($$4 \leq n \leq \infty$$) (MSC2010) 57N25 Shapes (aspects of topological manifolds) 54B15 Quotient spaces, decompositions in general topology
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