Exotic superconnections and Riemann-Roch-Grothendieck

  • Jean-Michel Bismut
Part of the Progress in Mathematics book series (PM, volume 305)


The purpose of this chapter is to establish the main result of this book, i.e., we give a Riemann-Roch-Grothendieck formula for the class \(\{\alpha_{g,t}\} \in H^{(=)}_{\rm{BC}}\) (S,C). When \({\bar\partial}^{M} {\partial^{M}} \omega^{M} = 0\), this result was already established in Theorem 5.2.1 using elliptic superconnections. The introduction in  Chapter 9 of hypoelliptic superconnections did not allow us to eliminate this assumption.


Heat Kernel Uniform Estimate Uniform Bound Scalar Part Obvious Extension 
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Copyright information

© Springer Basel 2013

Authors and Affiliations

  • Jean-Michel Bismut
    • 1
  1. 1.Département de MathématiqueUniversité Paris-SudOrsayFrance

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