Verdier quotients of Calabi-Yau categories from quivers with potential

TL;DR

This paper investigates a class of triangulated categories derived from quivers with potential associated to marked surfaces, focusing on their t-structures, exchange graphs, and the preservation of Koszul isomorphism under Verdier quotients.

Contribution

It introduces a new perspective on Verdier quotients of 3-Calabi-Yau categories from quivers with potential, analyzing their t-structures and exchange graphs, and proves the invariance of Koszul isomorphism.

Findings

The exchange graphs of hearts and silting objects are studied in these categories.

The Koszul isomorphism between exchange graphs is preserved under Verdier quotients.

The paper provides a combinatorial description linking quivers with potential to Calabi-Yau categories.

Abstract

We study a class of triangulated categories obtained as Verdier quotients of 3-Calabi-Yau categories combinatorially described by quivers with potential from (decorated) marked surfaces. We study their bounded t-structures and consider in particular the exchange graphs of hearts and silting objects, and show that the Koszul isomorphism between these graphs is preserved under Verdier quotient.