Hochschild and cyclic homology of Steinberg algebras of ample groupoids decompose in terms of groupoid homology, and for Exel-Pardo algebras these invariants and K-theory are computed by explicit cones and exact sequences.
Ample groupoids, topological full groups, algebraic K-theory spectra and infinite loop spaces
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
Inspired by work of Szymik and Wahl on the homology of Higman-Thompson groups, we establish a general connection between ample groupoids, topological full groups, algebraic K-theory spectra and infinite loop spaces, based on the construction of small permutative categories of compact open bisections. This allows us to analyse homological invariants of topological full groups in terms of homology for ample groupoids. Applications include complete rational computations, general vanishing and acyclicity results for group homology of topological full groups as well as a proof of Matui's AH-conjecture for all minimal, ample groupoids with comparison.
citation-role summary
background 1
citation-polarity summary
fields
math.KT 1years
2024 1verdicts
CONDITIONAL 1roles
background 1polarities
unclear 1representative citing papers
citing papers explorer
-
Homology of Steinberg algebras
Hochschild and cyclic homology of Steinberg algebras of ample groupoids decompose in terms of groupoid homology, and for Exel-Pardo algebras these invariants and K-theory are computed by explicit cones and exact sequences.