Measuring complexity of curves on surfaces

Max Neumann-Coto; Macarena Covadonga Robles Arenas

Measuring complexity of curves on surfaces

Geometric Topology 2018-07-20 v2

Authors: Max Neumann-Coto , Macarena Covadonga Robles Arenas

Abstract

We consider the relations between different measures of complexity for free homotopy classes of curves on a surface $\Sigma$ , including the minimum number of self-intersections, the minimum length of the words representing them in a geometric presentation of $\pi_1(\Sigma)$ , and the minimum degree of the coverings of $\Sigma$ to which they lift as embeddings.

Keywords

intersection theory on moduli spaces curves differential geometry

Cite

@article{arxiv.1712.06671,
  title  = {Measuring complexity of curves on surfaces},
  author = {Max Neumann-Coto and Macarena Covadonga Robles Arenas},
  journal= {arXiv preprint arXiv:1712.06671},
  year   = {2018}
}

Comments

14 pages,12 figures. Exposition has been improved giving more details and examples

Measuring complexity of curves on surfaces

Abstract

Keywords

Cite

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