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arXiv · 2402.06970

Index theory for Heisenberg elliptic and transversally Heisenberg elliptic operators from $KK$-theoretic viewpoint

Minjie Tian
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Abstract

This research comprehensively describes the basic theory of transversally Heisenberg elliptic operators, and investigates the index theory of Heisenberg elliptic and transversally Heisenberg elliptic operators from the perspective of $KK$-theory, applying Kasparov's methodology. Moreover, the analysis methodically examines specific conditions, with a focus on the Fourier transform of the nilpotent group $C^{\ast}$-algebra. We demonstrate enhanced methods for analyzing the hypoellipticity of operators, presenting a robust framework for defining and understanding transversal Heisenberg ellipticity in a $KK$-theoretic context. This work provides a solid foundation for future research into the properties of hypoelliptic differential operators in complicated manifolds.

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Minjie Tian. 2024-11-09. Index theory for Heisenberg elliptic and transversally Heisenberg elliptic operators from $KK$-theoretic viewpoint. https://doi.org/10.1142/s1793525324500511

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