Measuring complexity of curves on surfaces
Measuring complexity of curves on surfaces
复制标题
测量曲面上曲线的复杂性
作者：
Macarena Arenas;Max Neumann
We consider the relations between different measures of complexity for free homotopy classes of curves on a surface Σdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$Sigma $$end{document}, including the minimum number of self-intersections, the minimum length of the words representing them in π1(Σ)documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$pi _1(Sigma )$$end{document}, and the minimum degree of the coverings of Σdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$Sigma $$end{document} to which they lift as embeddings.
We consider the relations between different measures of complexity for free homotopy classes of curves on a surface Σdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$Sigma $$end{document}, including the minimum number of self-intersections, the minimum length of the words representing them in π1(Σ)documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$pi _1(Sigma )$$end{document}, and the minimum degree of the coverings of Σdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$Sigma $$end{document} to which they lift as embeddings.