Topology of angle valued maps, bar codes and Jordan blocks
arXiv:1303.4328
Abstract
In this paper one presents a collection of results about the "bar codes" and "Jordan blocks" introduced by Burghelea-Day as "computer friendly" invariants of a tame angle-valued map and one relates these invariants to the Betti numbers, Novikov Betti numbers and the monodromy of the underlying space and map. Among others, one organizes the bar codes as two configurations of points in C\0 and one establishes their main properties: stability property and when the underlying space is a closed topological manifold, Poincaré duality property. One also provides an alternative "computer friendly" definition of the monodromy of an angle valued map based on the algebra of linear relations as well as a refinement of Morse and Morse-Novikov inequalities.
Latex, 65 pages, 9 figures. arXiv admin note: text overlap with arXiv:1202.1208, additional comments in introduction, typos corrected and minor improvements in some proofs
References in corpus (2)
Cited by in corpus (7)
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