Cobordism invariance of topological edge-following states

We prove that a spectral gap-filling phenomenon occurs whenever Hamiltonian operator encounters coarse index obstruction upon compression to domain with boundary. Furthermore, the spectra contribute quantised current channels, which follow and are localised at possibly complicated This is shown be insensitive deformations of boundary, so generic for magnetic Laplacians modelling quantum Hall systems Chern topological insulators. A key construction quasi-equivariant version Roe's algebra locally compact finite propagation operators.