Bolibruch Impossibility Theorem
Revealing an obstruction for realization of a matrix group as the monodromy of a Fuchsian system on .

Degree (Chern class) of a complex bundle vs. that of a subbundle. The total trace of residues of a meromorphic connexion.

Linear algebra: Monoblock operators and their invariant subspaces.

Local theory revisited: local invariant subbundles of a (resonant) Fuchsian singularity in the Poincaré–Dulac–Levelt normal form.

Bolibruch connexions on the trivial bundle: theorem on the spectra of residues.

Three Matrices
: the Bolibruch Counterexample.
Reading: Section 18E from the book (printing disabled).
Refresh your memory: Sections 16C–16D (local theory), 17E17I (degree of bundles)