Topological Persistence for Circle-Valued Maps

@article{Burghelea2013TopologicalPF,
  title={Topological Persistence for Circle-Valued Maps},
  author={Dan Burghelea and Tamal K. Dey},
  journal={Discrete \& Computational Geometry},
  year={2013},
  volume={50},
  pages={69-98}
}
We study circle-valued maps and consider the persistence of the homology of their fibers. The outcome is a finite collection of computable invariants which answer the basic questions on persistence and in addition encode the topology of the source space and its relevant subspaces. Unlike persistence of real-valued maps, circle-valued maps enjoy a different class of invariants called Jordan cells in addition to bar codes. We establish a relation between the homology of the source space and of… 

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