Computing shortest words via shortest loops on hyperbolic surfaces

@article{Yin2011ComputingSW,
  title={Computing shortest words via shortest loops on hyperbolic surfaces},
  author={Xiaotian Yin and Yinghua Li and Wei Han and Feng Luo and Xianfeng Gu and Shing-Tung Yau},
  journal={Computer-Aided Design},
  year={2011},
  volume={43},
  pages={1449-1456}
}
Given a loop on a surface, its homotopy class can be specified as a word consisting of letters representing the homotopy group generators. One of the interesting problems is how to compute the shortest word for a given loop. This is an NP-hard problem in general. However, for a closed surface that allows a hyperbolic metric and is equipped with a canonical set of fundamental group generators, the shortest word problem can be reduced to finding the shortest loop that is homotopic to the given… CONTINUE READING

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