论文标题
Bismut-Cheeger ETA表格及其应用的扩展变异公式
An extended variational formula for the Bismut-Cheeger eta form and its applications
论文作者
论文摘要
本文的目的是通过允许旋转$^c $ dirac运算符被同构式矢量捆绑扭曲，并建立$ \ \ m i \ mathbb {z Z} _2 $ graded Additivity of Bissut-Cheegaut-Cheegaut-Cheegegaut-Cheegegaegega，则本文的目的是扩展我们先前在bismut-cheeger eta形式的变化公式的工作，而无需内核捆绑。使用这些结果，我们提供了替代证明，即差异$ k $ - 理论中的分析指数是一个定义明确的组同态，而Riemann-Roch-roch-grothendieck Theorem in $ \ Mathbb {r}/\ Mathbb {z}} $ k $ k $ - theore。
The purpose of this paper is to extend our previous work on the variational formula for the Bismut-Cheeger eta form without the kernel bundle assumption by allowing the spin$^c$ Dirac operators to be twisted by isomorphic vector bundles, and to establish the $\mathbb{Z}_2$-graded additivity of the Bismut-Cheeger eta form. Using these results, we give alternative proofs of the fact that the analytic index in differential $K$-theory is a well defined group homomorphism, and the Riemann-Roch-Grothendieck theorem in $\mathbb{R}/\mathbb{Z}$ $K$-theory.
