# Stability structures, motivic Donaldson-Thomas invariants and cluster transformations

@article{Kontsevich2008StabilitySM, title={Stability structures, motivic Donaldson-Thomas invariants and cluster transformations}, author={M. Kontsevich and Y. Soibelman}, journal={arXiv: Algebraic Geometry}, year={2008} }

We define new invariants of 3d Calabi-Yau categories endowed with a stability structure. Intuitively, they count the number of semistable objects with fixed class in the K-theory of the category ('number of BPS states with given charge' in physics language). Formally, our motivic DT-invariants are elements of quantum tori over a version of the Grothendieck ring of varieties over the ground field. Via the quasi-classical limit 'as the motive of affine line approaches to 1' we obtain numerical DT… Expand

#### 718 Citations

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