LAUSR

In this paper, we investigate topological aspects of indices of twisted geometric operators on manifolds equipped with fibered boundaries. We define K -groups relative to the pushforward for boundary fibration, and show that indices of twisted geometric operators, defined by complete $$\Phi $$ Φ or edge metrics, can be regarded as the index pairing over these K -groups. We also prove various properties of these indices using groupoid deformation techniques. Using these properties, we give an application to the localization problem of signature operators for singular fiber bundles.