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Nathan Bowler

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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.

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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
02.7	Excluded minors for representability, truncation.