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Let $E$ be a Clifford module with Clifford multiplication $c$. On page 117 of Heat Kernels and Dirac Operators it is claimed that "any operator satisfying \begin{equation}\tag{1} \forall f \in C^\inft …

I have some questions concerning the definition of Clifford super-connections in Heat Kernels and Dirac Operators: Definition 3.39. If $A$ is a super-connection on a Clifford module $E\to M$, we say …

I assume that the question in the title is clear, so let me talk about its relevance: According to theorem 4.3 in Heat Kernels and Dirac Operators the index theorem \begin{equation}\tag{1} \mathrm{ind …

The authors of Heat kernels and Dirac operators chose to consider a generalized Laplacian $H$ on a bundle $E\otimes|\Lambda|^{1/2}$ and heat kernels of $H$ are defined to be sections of $(E\otimes|\La …

Fix a Clifford module bundle $E$ on a compact Riemannian manifold $M$ and let $D_0$ and $D_1$ be two Dirac operators (compatible with the Clifford action). The proof of the Atiyah-Singer index theorem …