The following preprint: M. Grandis, "An intrinsic homotopy theory for simplicial complexes with applications to image processing" is available at: ftp://pitagora.dima.unige.it/WWW/FTP/GRANDIS/ as: Lnk.Nov98.ps *** Abstract. A simplicial complex is a set equipped with a down-closed family of distinguished finite subsets; this structure is mostly viewed as codifying a triangulated space. Here, this structure is used directly to describe "spaces" of interest in various applications, where the associated triangulated space would be misleading. An intrinsic homotopy theory, not based on topological realisation, is introduced. The applications considered here are aimed at metric spaces and digital topology; concretely, at image processing and computer graphics. A metric space X has a structure t_e(X) of simplicial complex at each "resolution" e > 0; the resulting n-homotopy group \pi_n(t_e(X)) detects those singularities which can be captured by an n-dimensional grid, with edges bound by e; this works equally well for continuous or discrete regions of euclidean spaces. *** Comments would be appreciated. In particular, I am uneasy about a question of terminology. In my opinion, the term "simplicial complex", quite appropriate when the structure is viewed as codifying a triangulated space, is unfit when such objects are treated as "spaces" in themselves (somewhat close to bornological spaces, which have similar axioms on objects and maps). In other words, "simplicial complex" should not refer to the category itself, say C, but to its usual embedding in Top, the simplicial realisation. The two aspects may clash, e.g. with respect to initial or final structures: the coarse C-object on three points (final structure, all parts are distinguished) is realised as a euclidean triangle; a C-subobject is sufficient to produce a topological subspace (a regular subobject in Top), but a C-subspace (a regular subobject in C) is a stronger notion. Moreover, from a more concrete point of view, the simplicial realisation is quite inappropriate in most of the applications considered in this work. The opposition "C-object / simplicial complex" is in part similar to "sequence / series": the second term refers to a more specific view & use of the same data; the clashing of the opposition is particularly evident in the notions of convergence, for a sequence or a series. That's why I am calling a C-object a "combinatorial space". (The term "combinatorial complex" has also been used for simplicial complex; and I wanted a term of the form "attribute + space", to use freely of topological terms like discrete, coarse, subspace...) But of course it is embarassing to propose a new term for a classical notion. Marco Grandis