Cohomology and extensions of ordered groupoids

2017/02/21 by Bernard Oduoku Bainson, Bainson, B. O., N. D. Gilbert +1
Mathematics · #20L05 #Advanced Operator Algebra Research #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1702.06333

openalex publication_date 2017/02/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We adapt and generalise results of Loganathan on the cohomology of inverse semigroups to the cohomology of ordered groupoids. We then derive a five-term exact sequence in cohomology from an extension of ordered groupoids, and show that this sequence leads to a classification of extensions by a second cohomology group. Our methods use structural ideas in cohomology as far as possible, rather than computation with cocycles.

Related

• The homology of principally directed ordered groupoids
• A seven-term exact sequence for the cohomology of a group extension
• Ordered groupoids and the holomorph of an inverse semigroup
• Double groupoid cohomology and extensions
• Ordered groupoid quotients and congruences on inverse semigroups