Graph Representations and Topology of Real and Angle Valued Maps
نویسندگان
چکیده
In this paper we review the definition of the invariants “bar codes” and “Jordan cells” of real and angle valued tame maps as proposed in [1] and [4] and prove the homotopy invariance of the sums ]Bc r + ]Bo r−1 and of the set of Jordan cells. Here Bc r resp. Bo r denote the sets of closed resp. open bar codes in dimension r. In addition we provide calculation of some familiar topological invariants in terms of bar codes and Jordan cells. The presentation provides a different perspective on Morse–Novikov theory based on critical values, bar codes and Jordan cells rather than on critical points instantons and closed trajectories of a gradient of a real or angle valued map.
منابع مشابه
Topology of Real and Angle Valued Maps and Graph Representations
Using graph representations a new class of computable topological invariants associated with a tame real or angle valued map were recently introduced, providing a theory which can be viewed as an alternative to MorseNovicov theory for real or angle valued Morse maps. The invariants are ”barcodes” and ”Jordan cells”. From them one can derive all familiar topological invariants which can be deriv...
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