Tilting and Refined Donaldson-Thomas Invariants
Magnus Engenhorst
TL;DR
This paper investigates how tilting in the derived category of Ginzburg algebras affects Donaldson-Thomas invariants, establishing conditions under which these invariants are independent of the central charge.
Contribution
It provides new conditions for tilting in the derived category that ensure the invariance of refined Donaldson-Thomas invariants across different central charges.
Findings
Conditions for stable objects to define simple tilts from A to A[-1]
Proof of invariance of refined Donaldson-Thomas invariants under certain tilts
Link between tilting sequences and invariance of invariants
Abstract
We study tilting for the heart A of the canonical t-structure of the finite-dimensional derived category of the Ginzburg algebra for a quiver with potential (Q,W). We give conditions on that the stable objects for a central charge on A define a sequence of simple tilts from A to A[-1]. On that conditions the refined Donaldson-Thomas invariant associated to (Q,W) is independent of the chosen central charge.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Molecular spectroscopy and chirality · Nonlinear Waves and Solitons