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Large 1-systems
of curves in nonorientable surfaces
Sarah Ruth Nicholls, Nancy Scherich and Julia Shneidman |
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Vol. 16 (2023), No. 1, 127–139
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Abstract |
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A well-known 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 nonorientable surfaces, which are exactly those surfaces that contain a Möbius band. We generalize a construction of Malestein, Rivin and Theran to nonorientable surfaces to exhibit a lower bound for the maximum number of curves that pairwise intersect 0 or 1 times in a generic nonorientable surface. |
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Keywords
nonorientable surfaces, 1-systems of curves
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Mathematical Subject Classification
Primary: 57M99
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Milestones
Received: 21 September 2021
Revised: 14 March 2022
Accepted: 15 March 2022
Published: 14 April 2023
Communicated by Frank Morgan
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Authors |
| Sarah Ruth Nicholls | |
| Wake Forest University Winston-Salem, NC United States |
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| Nancy Scherich | |
| ICERM Brown University Providence, RI United States |
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| Julia Shneidman | |
| Rutgers University Hill Center for the Mathematical Sciences Piscataway, NJ United States |
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| © 2023 MSP (Mathematical Sciences Publishers). |
