# Conormal homology of manifolds with corners

### Thomas Schick

Universität Göttingen, Germany### Mario Velasquez

Universidad Nacional de Colombia, Bogotá, Colombia

## Abstract

Given a manifold with corners $X$, we associate 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 construct 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.

## Cite this article

Thomas Schick, Mario Velasquez, Conormal homology of manifolds with corners. J. Noncommut. Geom. 17 (2023), no. 4, pp. 1425–1436

DOI 10.4171/JNCG/520