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Topological dynamics in neurobiology.

A mathematical model consisting of three interrelated parts is proposed. The first part is the space of representation in terms of physico-chemical elements, the second the static topologies imposed on this space, and the third the dynamics of the representation space endowed with topological properties. In the present study various relevant mathematical concepts are introduced for each of the three parts. The classification of generic elements for the representation spaces, the group representation of the pathways in terms of braid groups and an algebra for the n-dimensional spatial and m-dimensional temporal space of the dynamic system for the neural activities form the basic ideas of the model. Some experimental results are interpreted as illustrative examples of the formal ideas.