2020/04/08 by Emerson G. Escolar, Escolar, Emerson G., Killian Meehan +3 · 1 citation
Mathematics · #16G20 #55N99 #Algebraic Topology (math.AT) #FOS: Mathematics #Representation Theory (math.RT) #math.AT #math.RT #msc:16G20 #msc:55N99
paper · pdf · doi:10.48550/arxiv.2004.03840
15 pages
arxiv created 2020/04/08 · arxiv updated 2020/04/09
In order to better understand and to compare interleavings between persistence modules, we elaborate on the algebraic structure of interleavings in general settings. In particular, we provide a representation-theoretic framework for interleavings, showing that the category of interleavings under a fixed translation is isomorphic to the representation category of what we call a shoelace. Using our framework, we show that any two interleavings of the same pair of persistence modules are themselves interleaved. Furthermore, in the special case of persistence modules over ℤ, we show that matchings between barcodes correspond to the interval-decomposable interleavings.