Journal
DISCRETE & COMPUTATIONAL GEOMETRY
Volume 50, Issue 1, Pages 69-98Publisher
SPRINGER
DOI: 10.1007/s00454-013-9497-x
Keywords
Topological persistence; Persistence for circle-valued maps; Bar codes; Jordan cells
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Funding
- NSF [CCF-0915996]
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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.
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