Floer-type bipersistence modules and rectangle barcodes

2023/12/13 by Koeda, Kanta, Orita, Ryuma, Yashiro, Kanon
#16G20 #55N31 #57R58 #58E05 #Algebraic Topology (math.AT) #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2312.07847

Abstract

In this paper, we show that the pointwise finite-dimensional two-parameter persistence module \mathbbHF_*^{(\bullet,\bullet]}, defined in terms of interlevel filtered Floer homology, is rectangle-decomposable. This allows for the definition of a barcode B_*^{(\bullet,\bullet]} consisting only of rectangles in ℝ² associated with \mathbbHF_*^{(\bullet,\bullet]}. We observe that this rectangle barcode contains information about Usher's boundary depth and spectral invariants developed by Oh, Schwarz, and Viterbo. Moreover, we establish relevant stability results, particularly concerning the bottleneck distance and Hofer's distance.

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