# Computations of characteristic classes and genera: A practical toolkit for beginners and practitioners

Hisham Sati, Silviu-Marian Udrescu, Erika Zogla – GJM, Volume 3, Issue 2 (2018), 60-93.

This paper provides explicit combinatorial expansions of the Chern classes, Pontrjagin classes, Chern character, as well as the Chern character and Chern classes of a tensor product of two vector bundles. One will also find expansions of the $\widehat{A}$-genus, L-genus, Todd genus, their twisted forms, as well as relations among the three genera. The computational methods are elementary, but we hope that the clearly displayed and ready-to-use results — which do not seem to be otherwise available — will be useful. This is the first part of research based on the undergraduate project of the second and third authors advised by the first author.

Categories: Issue2, 2018