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Large 1-systems of curves in nonorientable surfaces

Sarah Ruth Nicholls, Nancy Scherich and Julia Shneidman

Vol. 16 (2023), No. 1, 127–139
Abstract

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.

Keywords
nonorientable surfaces, 1-systems of curves
Mathematical Subject Classification
Primary: 57M99
Milestones
Received: 21 September 2021
Revised: 14 March 2022
Accepted: 15 March 2022
Published: 14 April 2023

Communicated by Frank Morgan
Authors
Sarah Ruth Nicholls
Wake Forest University
Winston-Salem, NC
United States
Nancy Scherich
ICERM
Brown University
Providence, RI
United States
Julia Shneidman
Rutgers University
Hill Center for the Mathematical Sciences
Piscataway, NJ
United States