arXiv Open Access 2016

A counterexample to the extension space conjecture for realizable oriented matroids

Gaku Liu

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Abstrak

The extension space conjecture of oriented matroid theory states that the space of all one-element, non-loop, non-coloop extensions of a realizable oriented matroid of rank $d$ has the homotopy type of a sphere of dimension $d-1$. We disprove this conjecture by showing the existence of a realizable uniform oriented matroid of high rank and corank 3 with disconnected extension space.

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math.CO

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Gaku Liu

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APA MLA BibTeX

Liu, G. (2016). A counterexample to the extension space conjecture for realizable oriented matroids. https://arxiv.org/abs/1606.05033

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Informasi Jurnal

Tahun Terbit: 2016
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓