This is a survey of the book Donaldson-Thomas invariants DT ( ) Z 'count' -(semi)stable coherent sheaves with Chern character on a Calabi-Yau 3-fold X. They are unchanged under deformations of X. The conventional definition works only for classes with no strictly -semistable sheaves. Behrend showed that DT ( ) can be written as a weighted Euler characteristic M st ( ), M st ( ) of the stable moduli scheme M st ( ) by a constructible function M st ( ) we call the 'Behrend function'.
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Dominic Joyce (2011) studied this question.
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