Title: Potential functions on Grassmannians of planes and cluster transformations,
Abstract: With a triangulation of a planar polygon with $n$ sides, one can associate an
integrable system on the Grassmannian of 2-planes in an $n$-space. In this
paper, we show that the potential functions of Lagrangian torus fibers of the
integrable systems associated with different triangulations glue together by
cluster transformations. We also prove that the cluster transformations
coincide with the wall-crossing formula in Lagrangian intersection Floer
theory.