Abstract We introduce weighted cycles on weaves of general Dynkin types and define a skew‐symmetrizable intersection pairing between weighted cycles. We prove that weighted cycles on a weave form a Laurent polynomial algebra and construct a quantization of this algebra using the skew‐symmetric intersection pairing in the simply‐laced case. We define merodromies along weighted cycles as functions on the decorated flag moduli space of the weave. We relate weighted cycles to cluster variables in a cluster algebra and prove that mutations of weighted cycles are compatible with mutations of cluster variables.
Daping Weng (Mon,) studied this question.