(HoRSe seminar) On the calculus underlying Donaldson-Thomas theory I
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Tue, 16/11/2010 14:00 |
Kai Behrend (Vancouver) |
Algebraic and Symplectic Geometry Seminar  |
SR1 |
| On a manifold there is the graded algebra of polyvector fields with its Lie-Schouten bracket, and the module of de Rham differentials with exteriour differentiation. This package is called a "calculus". The moduli space of sheaves (or derived category objects) on a Calabi-Yau threefold has a kind of "virtual calculus" on it, at least conjecturally. In particular, this moduli space has virtual de Rham cohomology groups, which categorify Donaldson-Thomas invariants, at least conjecturally. We describe some attempts at constructing such a virtual calculus. This is work in progress. | |||