Sergei Yakovenko's blog: on Math and Teaching

Wednesday, March 26, 2008

Lecture 6 (Thu, Mar 27, 2008)

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)

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