  Syntactic theory has traditionally adopted a constructivist approach, in
which a set of atomic elements are manipulated by combinatory operations to
yield derived, complex elements. Syntactic structure is thus seen as the result
or discrete recursive combinatorics over lexical items which get assembled into
phrases, which are themselves combined to form sentences. This view is common
to European and American structuralism (e.g., Benveniste, 1971; Hockett, 1958)
and different incarnations of generative grammar, transformational and
non-transformational (Chomsky, 1956, 1995; and Kaplan & Bresnan, 1982; Gazdar,
1982). Since at least Uriagereka (2002), there has been some attention paid to
the fact that syntactic operations must apply somewhere, particularly when
copying and movement operations are considered. Contemporary syntactic theory
has thus somewhat acknowledged the importance of formalizing aspects of the
spaces in which elements are manipulated, but it is still a vastly
underexplored area. In this paper we explore the consequences of
conceptualizing syntax as a set of topological operations applying over spaces
rather than over discrete elements. We argue that there are empirical
advantages in such a view for the treatment of long-distance dependencies and
cross-derivational dependencies: constraints on possible configurations emerge
from the dynamics of the system.
