The Chern-Gauss-Bonnet theorem can be deduced from the Atiyah-Singer theorem by applying it to the differential operator $d+d^\*$ mapping from sum of even powers of the exterior sheaf to the sum of odd powers over a compact manifold.


A few months ago, I came across a name for this operator, but I haven't seen it referred to it again with that name. Is there a standard name for this operator?



What is the differential operator $d+d^*$ called?
The operator is defined in Example 2.1.18 [here](https://www3.nd.edu/%7Elnicolae/ind-thm.pdf) and called the *Hodge-de Rham operator*. While this might not be an authoritative reference, a Google search reveals a lot of results which use this term.


