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...rac_operator|Dirac operators]], $\partial\!\!\!/_M$. The (Clifford-linear) Dirac operator can be considered as a representative of the fundamental class $[M ...rs above can then be defined as the indices of the (Clifford-linear) Dirac operators obtained by twisting with the corresponding vector bundles.

... multiplication of elements in $Spin(n)$ on $Cl(n)$. The [[Dirac Operators|Dirac operator]] $D$ then acts on the space of sections $\Gamma(S)$. The kernel o ...ich yields the formula $D^2 = \nabla^*\nabla + \frac{1}{4}scal(M)$ for the Dirac operator $D$. Here $\nabla^*\nabla$ denotes the connection Laplacian which