• Corpus ID: 235212110

A Variational Loop Shrinking Analogy for Handle and Tunnel Detection and Reeb Graph Construction on Surfaces

@article{Weinrauch2021AVL,
  title={A Variational Loop Shrinking Analogy for Handle and Tunnel Detection and Reeb Graph Construction on Surfaces},
  author={Alexander Weinrauch and Hans-Peter Seidel and Daniel Mlakar and Markus Steinberger and Rhaleb Zayer},
  journal={ArXiv},
  year={2021},
  volume={abs/2105.13168}
}
The humble loop shrinking property played a central role in the inception of modern topology but it has been eclipsed by more abstract algebraic formalism. This is particularly true in the context of detecting relevant non- contractible loops on surfaces where elaborate homological and/or graph theoretical constructs are favored in algorithmic solutions. In this work, we devise a variational analogy to the loop shrinking property and show that it yields a simple, intuitive, yet powerful… 

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