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Systems of curves on non-orientable surfaces

Xiao Chen Tsinghua University

Geometric Analysis and Geometric Topology mathscidoc:2408.15001

We show that the order of the cardinality of maximal complete $1$-systems of loops on non-orientable surfaces is $\sim |\chi|^{2}$. In particular, we determine the exact cardinality of maximal complete $1$-systems of loops on punctured projective planes. To prove these results, we show that the cardinality of maximal systems of arcs pairwise-intersecting at most once on a non-orientable surface is $2|\chi|(|\chi|+1)$.
Systems of curves; arc complexes; hyperbolic geometry; mapping class groups; Teichmüller spaces.
[ Download ] [ 2024-08-01 16:28:27 uploaded by SmarcaChern ] [ 129 downloads ] [ 0 comments ]
  • 23 pages, 18 figures.
@inproceedings{xiaosystems,
  title={Systems of curves on non-orientable surfaces},
  author={Xiao Chen},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20240801162828021985770},
}
Xiao Chen. Systems of curves on non-orientable surfaces. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20240801162828021985770.
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