Donaldson-Thomas invariants via microlocal geometry
-- Kai Behrend

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We define moduli spaces with self-dual or symmetric obstruction theories.
The main examples are the moduli spaces of sheaves one uses to define
Donaldson-Thomas invariants.  We show how ideas from microlocal geometry
give rise to a canonically defined constructible integer-valued function on
such a moduli space.  We prove that the virtual degree of a space with
symmetric obstruction theory (i.e., the Donaldson-Thomas invariant) is equal
to the Euler characteristic of the moduli space, weighted by the
constructible function.  In particular, it makes sense to generalize
Donaldson-Thomas type invariants to non-compact moduli spaces.   This makes
Donaldson-Thomas type invariants amenable to computations via
stratifications.