# Bolibruch Impossibility Theorem

Revealing an obstruction for realization of a matrix group as the monodromy of a Fuchsian system on $\mathbb C P^1$.

1. Degree (Chern class) of a complex bundle vs. that of a subbundle. The total trace of residues of a meromorphic connexion.
2. Linear algebra: Monoblock operators and their invariant subspaces.
3. Local theory revisited: local invariant subbundles of a (resonant) Fuchsian singularity in the Poincaré–Dulac–Levelt normal form.
4. Bolibruch connexions on the trivial bundle: theorem on the spectra of residues.
5. Three Matrices $4\times 4$: the Bolibruch Counterexample.

Reading: Section 18E from the book (printing disabled).

Refresh your memory: Sections 16C16D (local theory), 17E-17I (degree of bundles)