Mathai-Quillen's Thom form and Atiyah-Hirzebruch's Riemann-Roch theorem

Mathai-Quillen's Thom form and Atiyah-Hirzebruch's Riemann-Roch theorem

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Guangbo Xu, Princeton University
Fine Hall 314

After Hirzebruch's generalization of the classical Riemann-Roch formula, Grothendieck extended this result to a relative version. Then Atiyah and Hirzebruch gave a "differentiable analogue" of Grothendieck's theorem, which is called Atiyah-Hirzebruch's Riemann-Roch theorem. In spite of the original topological proof, I will present another one, in a more differential-geometric flavor, using Mathai-Quillen's construction of the Thom form.