The Pimsner-Voiculescu sequence for coactions of compact Lie groups

TL;DR

This paper extends the Pimsner-Voiculescu sequence to a tower for coactions of compact Lie groups, demonstrating that such coactions satisfy the Baum-Connes property, thus advancing the understanding of equivariant KK-theory.

Contribution

It introduces a generalized Pimsner-Voiculescu tower for coactions of compact Hodgkin-Lie groups, linking it to the Baum-Connes conjecture.

Findings

Established a Pimsner-Voiculescu tower for coactions of compact Lie groups.

Proved that coactions of compact Hodgkin-Lie groups satisfy the Baum-Connes property.

Connected the tower construction to equivariant KK-theory and the Hodgkin condition.

Abstract

The Pimsner-Voiculescu sequence is generalized to a Pimsner-Voiculescu tower describing the $KK$-category equivariant with respect to coactions of a compact Lie group satisfying the Hodgkin condition. A dual Pimsner-Voiculescu tower is used to show that coactions of a compact Hodgkin-Lie group satisfy the Baum-Connes property.