Large 1-systems of Curves in Non-orientable Surfaces

Sarah Ruth Nicholls; Nancy Scherich; Julia Shneidman

doi:10.2140/involve.2023.16.127

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arXiv · 2109.04882

Large 1-systems of Curves in Non-orientable Surfaces

Sarah Ruth Nicholls·Nancy Scherich·Julia Shneidman

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Abstract

A longstanding avenue of research in orientable surface topology is to create and enumerate collections of curves in surfaces with certain intersection properties. We look for similar collections of curves in non-orientable surfaces. A surface is non-orientable if and only if it contains a M\"obius band. We generalize a construction of Malestein-Rivin-Theran to non-orientable surfaces to exhibit a lower bound for the maximum number of curves that pairwise intersect 0 or 1 times in a generic non-orientable surface.

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Sarah Ruth Nicholls, Nancy Scherich, Julia Shneidman. 2021-09-10. Large 1-systems of Curves in Non-orientable Surfaces. https://doi.org/10.2140/involve.2023.16.127

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