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## Nathan Bowler

### Lecture course "Infinite Matroid Theory", summer semester 2015

#### Exercise sheets (Deadlines in brackets)

There will be one exercise sheet per week.

Here are the exercise sheets:
week 1 week 2 week 3 week 4 week 5 week 6 week 7 week 8 week 9 week 10 week 11 week 12

#### Background material:

For information on finite matroids, see `Matroid Theory' by James Oxley. Papers about infinite matroids can be found here. The website for a previous version of this course is here.

#### Log:

 2.4 Overview, independence and basis axioms, basic examples 7.4 Other axiomatisations: circuits, closure etc. 9.4 Duality, definition of minors 14.4 Bases, independent sets and circuits of minors 16.4 Union and Intersection 21.4 The theorems of König, Hall and Menger 23.4 Scrawl systems and basic examples, duality 28.4 Minors of scrawl systems and algebraic cycle systems 30.4 Bases in scrawl systems, examples of hereditarily based systems 5.5 Equivalence of the axiomatisations 7.5 Definition of |G| 12.5 Properties of |G|, topological circuits 19.5 Topological circuits are circuits of M_{FB}* 21.5 Connectivity 26.5 2-Connectivity and torsos 28.5 Submodularity and trees of separations 9.6 The canonical tree decomposition into circuits, cocircuits and 3-connected torsos 11.6 The linking conjecture and the theorem of Aharoni and Berger 16.6 The Intersection, Packing/Covering and Covering conjectures 18.6 Proofs of special cases of the Covering and Linking Conjectures 23.6 Thin sums representability, quasibinary wild matroids 25.6 Properties of tame binary matroids 30.6 Affine compactness, paintability and representability 2.7 Excluded minors for representability, truncation.

 Impress 2017-10-17, Nathan Bowler