A Going-Down principle for ample groupoids and the Baum-Connes conjecture
Sign Up to like & getrecommendations! Published in 2020 at "Advances in Mathematics"
DOI: 10.1016/j.aim.2020.107314
Abstract: Abstract We study a Going-Down (or restriction) principle for ample groupoids and its applications. The Going-Down principle for locally compact groups was developed by Chabert, Echterhoff and Oyono-Oyono and allows to study certain functors, that… read more here.
Keywords: ample groupoids; connes conjecture; principle ample; baum connes ... See more keywords
Controlled K-theory for groupoids & applications to Coarse Geometry
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Functional Analysis"
DOI: 10.1016/j.jfa.2018.02.005
Abstract: We develop a generalization of quantitative $K$-theory, which we call controlled $K$-theory. It is powerful enough to study the $K$-theory of crossed product of $C^*$-algebras by action of \'etale groupoids and discrete quantum groups. In… read more here.
Keywords: baum connes; conjecture; controlled theory; coarse geometry ... See more keywords
Baum–Connes and the Fourier–Mukai transform
Sign Up to like & getrecommendations! Published in 2022 at "Illinois Journal of Mathematics"
DOI: 10.1215/00192082-9725548
Abstract: The Baum-Connes map for finitely generated free abelian groups is a K-theoretic analogue of the Fourier-Mukai transform from algebraic geometry. We describe this K-theoretic transform in the language of topological correspondences, and compute its action… read more here.
Keywords: fourier mukai; connes fourier; baum connes; mukai transform ... See more keywords