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arXiv · 2503.08020

Weighted Cycles on Weaves

Daping Weng
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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 for 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 with cluster variables in a cluster algebra and prove that mutations of weighted cycles are compatible with mutations of cluster variables.

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Daping Weng. 2025-03-11. Weighted Cycles on Weaves. https://arxiv.org/abs/2503.08020

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