Naive motivic Donaldson-Thomas type Hirzebruch classes and some problems

@article{Bussi2014NaiveMD,
  title={Naive motivic Donaldson-Thomas type Hirzebruch classes and some problems},
  author={Vittoria Bussi and Shoji Yokura},
  journal={arXiv: Algebraic Geometry},
  year={2014}
}
Donaldson-Thomas invariant is expressed as the weighted Euler characteristic of the so-called Behrend (constructible) function. In (2) Behrend introduced a Donaldson-Thomas type invariant for a mor- phism. Motivated by this invariant, we extend the motivic Hirzebruch class to naive Donaldson-Thomas type analogues. We also discuss a categorification of the Donaldson-Thomas type invariant for a morphism from a bivariant-theoretic viewpoint, and we finally pose some related questions for further… 
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