The Mayer-Vietoris Sequence for the Analytic Structure Group

2012/12/02 by Paul Siegel, Siegel, Paul · 3 citations
Mathematics · #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #K-Theory and Homology (math.KT) #math.KT

paper · pdf · doi:10.48550/arxiv.1212.0241

arxiv created 2012/12/02 · openalex publication_date 2012/12/02 · arxiv updated 2012/12/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We develop a Mayer-Vietoris sequence for the analytic structure group explored by Higson and Roe. Using explicit formulas for Mayer-Vietoris boundary maps, we give a new proof and generalizations of Roe's partitioned manifold index theorem.

Cited by

• Relative-partitioned index theorem
• The relative index in coarse index theory and submanifold obstructions to uniform positive scalar curvature
• Coarse Baum-Connes and warped cones: failure of surjectivity in odd degree

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• The Higson-Roe sequence for étale groupoids. I. Dual algebras and compatibility with the BC map
• Index theory in spaces of manifolds