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 its relevant subspaces with these invariants and provide a new algorithm to compute these invariants from an input matrix that encodes a circle-valued map on an input simplicial complex. © 2013 Springer Science+Business Media New York.
CITATION STYLE
Burghelea, D., & Dey, T. K. (2013). Topological Persistence for Circle-Valued Maps. Discrete and Computational Geometry, 50(1), 69–98. https://doi.org/10.1007/s00454-013-9497-x
Mendeley helps you to discover research relevant for your work.