Pith. sign in

REVIEW 1 cited by

A Homology Theory for Etale Groupoids

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv math/9905011 v1 pith:ZKTP4RZA submitted 1999-05-03 math.KT math.AT

Marius Crainic , Ieke Moerdijk This is my paper · ORCID
classification math.KTmath.AT
keywords etalegroupoidshomologyhomologiesspacestheoryactionsalgebra
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
read the original abstract

Etale groupoids arise naturally as models for leaf spaces of foliations, for orbifolds, and for orbit spaces of discrete group actions. In this paper we introduce a sheaf homology theory for etale groupoids. We prove its invariance under Morita equivalence, as well as Verdier duality between Haefliger cohomology and this homology. We also discuss the relation to the cyclic and Hochschild homologies of Connes' convolution algebra of the groupoid, and derive some spectral sequences which serve as a tool for the computation of these homologies.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Cup and cap products for cohomology and homology groups of ample groupoids

    math.OA 2024-11 conditional novelty 5.0 of 10

    Concrete cup and cap product formulas for ample groupoids are developed and applied to tiling-space cohomology computations and to an asymptotic-innerness invariant for C*-algebra automorphisms.

Pith tools