Decorated marked surfaces II: Intersection numbers and dimensions of Homs

2014/11/14 by Qiu, Yu, Zhou, Yu · 2 citations
#Category Theory (math.CT) #FOS: Mathematics #Geometric Topology (math.GT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1411.4003

Abstract

We study the 3-Calabi-Yau categories D arising from quivers with potential associated to a decorated marked surface S_\bigtriangleup introduced by the first author. We prove two conjectures in the prequel, that under a bijection between certain objects in D and certain arcs in S_\bigtriangleup, the dimensions of morphisms between these objects equal the intersection numbers between the corresponding arcs.

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