Conormal homology of manifolds with corners

• Published in: Journal of noncommutative geometry Vol. 17; no. 4; pp. 1425 - 1436
• Main Authors: Schick, Thomas, Velasquez, Mario
• Format: Journal Article
• Language: English
• Published: European Mathematical Society Publishing House 01-01-2023
• Subjects: Homology theory (Mathematics); Manifolds (Mathematics); Mathematical research; Germany
• ISSN: 1661-6952; 1661-6960
• DOI: 10.4171/jncg/520

Given a manifold with corners X , we associate to it the corner structure simplicial complex \Sigma_X . Its reduced K-homology is isomorphic to the K-theory of the C^* -algebra \mathcal{K}_b(X) of b-compact operators on X . Moreover, the homology of \Sigma_X is isomorphic to the conormal homology of X .
In this note, we construct for an arbitrary abstract finite simplicial complex \Sigma a manifold with corners X such that \Sigma_X\cong\Sigma . 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.