TL;DR
This paper introduces new formulas for computing coarse indices of twisted Dirac operators, linking $E$-theory and $K$-theory, and explores their implications for duality in operator algebras.
Contribution
It presents novel formulas for coarse indices using composition products in $E$-theory and module multiplications in $K$-theory, providing new index theoretic insights.
Findings
Formulas for coarse indices via $E$-theory composition product.
Formulas via module multiplication in $K$-theory.
Index theoretic interpretation of duality between Roe algebra and Higson corona.
Abstract
Several formulas for computing coarse indices of twisted Dirac type operators are introduced. One type of such formulas is by composition product in -theory. The other type is by module multiplications in -theory, which also yields an index theoretic interpretation of the duality between Roe algebra and stable Higson corona.
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