Kocutar, Juš (2025) Towards the Second Homology Theorem for Matroids. Bachelor's Thesis, Mathematics.
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Abstract
In the first part of this thesis we present the proofs of the path theorem and Tutte homotopy theorem concerning sequences of hyperplanes in a matroid. In the second part, we show the reformulations of the theorems in terms of homology groups of order complexes, following [2]. We find a replacement for the sublattice of the fourth class for the Tutte homotopy theorem and give a reformulation of the theorem. Using a computer program that we create, we find some necessary sublattices for the hypothetical second homology theorem to hold. We discuss how a second homology theorem might look like and we provide some tools that could be used in its proof.
| Item Type: | Thesis (Bachelor's Thesis) |
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| Supervisor name: | Lorscheid, O. and Top, J. |
| Degree programme: | Mathematics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 01 Jul 2025 07:58 |
| Last Modified: | 01 Jul 2025 07:58 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/35642 |
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