Geodesic
Naive motivic Donaldson--Thomas type Hirzebruch classes and some problems
Journal of Singularities, Tome 10 (2014), pp. 26-53

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Donaldson-Thomas invariant is expressed as the weighted Euler characteristic of the so-called Behrend (constructible) function. In 2009, Behrend introduced a Donaldson-Thomas type invariant for a morphism. 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 investigations. 
@article{10_5427_jsing_2014_10b,
     author = {Vittoria Bussi and Shoji Yokura},
     title = {Naive motivic {Donaldson--Thomas} type {Hirzebruch} classes and some problems},
     journal = {Journal of Singularities},
     pages = {26--53},
     publisher = {mathdoc},
     volume = {10},
     year = {2014},
     doi = {10.5427/jsing.2014.10b},
     url = {http://geodesic.mathdoc.fr/articles/10.5427/jsing.2014.10b/}
}
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Vittoria Bussi; Shoji Yokura. Naive motivic Donaldson--Thomas type Hirzebruch classes and some problems. Journal of Singularities, Tome 10 (2014), pp. 26-53. doi: 10.5427/jsing.2014.10b

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