Topological Coding in the Hippocampus

The brain constructs internal representations of the external world, and one essential element of efforts to understand neural processing focuses on understanding the nature of these internal representations. This chapter examines the currently available experimental evidence concerning the physiological and cognitive mechanisms of space representation in humans and in animals, and in particular, on the role of the hippocampus. The hippocampus is essential for the ability to navigate through space, and hippocampal neurons tend to fire in specific subregions of an animal’s environment. At the same time, it is not clear how the hippocampal representation of space is best described in terms of well-established mathematical definitions of space, nor is it clear whether the hippocampal representation is sufficient to construct a mathematical space. This chapter shows that, using only the times of spikes from hippocampal place cells, it is possible to construct a topological space, and it is argued that the hippocampus is specialized for computing a topological representation of the environment. Based on this observation, the chapter discusses the possibility of a constructive neural representation of a topological space.