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
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| 7.4 | Other axiomatisations: circuits, closure etc.
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| 9.4 | Duality, definition of minors
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| 14.4 | Bases, independent sets and circuits of minors
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| 16.4 | Union and Intersection
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| 21.4 | The theorems of König, Hall and Menger
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| 23.4 | Scrawl systems and basic examples, duality
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| 28.4 | Minors of scrawl systems and algebraic cycle systems
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| 30.4 | Bases in scrawl systems, examples of hereditarily based systems
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| 5.5 | Equivalence of the axiomatisations
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| 7.5 | Definition of |G|
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| 12.5 | Properties of |G|, topological circuits
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| 19.5 | Topological circuits are circuits of M_{FB}*
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| 21.5 | Connectivity
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| 26.5 | 2-Connectivity and torsos
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| 28.5 | Submodularity and trees of separations
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| 9.6 | The canonical tree decomposition into circuits, cocircuits and 3-connected torsos
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| 11.6 | The linking conjecture and the theorem of Aharoni and Berger
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| 16.6 | The Intersection, Packing/Covering and Covering conjectures
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| 18.6 | Proofs of special cases of the Covering and Linking Conjectures
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| 23.6 | Thin sums representability, quasibinary wild matroids
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| 25.6 | Properties of tame binary matroids
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| 30.6 | Affine compactness, paintability and representability
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| 02.7 | Excluded minors for representability, truncation.
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