A self-contained geometric proof of the wall-crossing formula via path-lifting rules for spectral networks, including spiral domains, with the charge lattice generated by A0-laminations.
Donaldson-Thomas theory for categories of homological dimension one with potential
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abstract
The aim of the paper is twofold. Firstly, we give an axiomatic presentation of Donaldson-Thomas theory for categories of homological dimension at most one with potential. In particular, we provide rigorous proofs of all standard results concerning the integration map, wall-crossing, PT-DT correspondence, etc. following Kontsevich and Soibelman. We also show the equivalence of their approach and the one given by Joyce and Song. Secondly, we relate Donaldson-Thomas functions for such a category with arbitrary potential to those with zero potential under some mild conditions. As a result of this, we obtain a geometric interpretation of Donaldson-Thomas functions in all known realizations, i.e. mixed Hodge modules, perverse sheaves and constructible functions.
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Wall-crossing formulas via spectral networks
A self-contained geometric proof of the wall-crossing formula via path-lifting rules for spectral networks, including spiral domains, with the charge lattice generated by A0-laminations.