Conormal homology of manifolds with corners

2021/11/26 by Thomas Schick, Schick, Thomas, Mario Velásquez +1 · 1 citation
Mathematics · Computer Science · #Homotopy and Cohomology in Algebraic Topology #Advanced Operator Algebra Research #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2111.13601

Abstract

Given a manifold with corners X, we associates to it the corner structure simplicial complex Σ_X. Its reduced K-homology is isomorphic to the K-theory of the C^*-algebra K_b(X) of b-compact operators on X. Moreover, the homology of Σ_X is isomorphic to the conormal homology of X. In this note, we constract for an arbitrary abstract finite simplicial complex Σ a manifold with corners X such that Σ_X≅ Σ. As a consequence, the homology and K-homology which occur for finite simplicial complexes also occur as conormal homology of manifolds with corners and as K-theory of their b-compact operators. In particular, these groups can contain torsion.

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