The fiber bundle theory is the fundamental method applied to the geodesic in mathematics or the gauge theory in physics. The theory could be applied as a useful method to understand and predict the emergent structures of a feature map, such as a visual map, in the brain. We introduce how the peculiar concepts in the fiber bundle theory or the gauge theory, such as the section and matter field, correspond with the attributes of a feature map, in the brain. Also, we show that the typical properties of an orientation preference map in the primary visual cortex can be explained through only the topological properties of the system.

Keywords: Neural networks, Structure of complex systems, Fiber bundle theory, Gauge theory