Do “lateral connections” in the cortex carry out topological information?

The observed massive presence of non-local lateral connections in the cerebral cortex is not compatible with the implicit assumption of flatness of most models, including models of associative areas. We suggest a novel hypothesis about the functional role of lateral connections in such areas: they may reflect a topological representations of the task space. In particular, we show how the topologic information, supported by long-range connections in associative areas, can represent spatial or metric knowledge. The power of the mechanism is demonstrated by describing an activation dynamics and showing the formation of bands of ocular dominance.