@inbook{92a25f1e207d42faa39d414348893aa9,
title = "Interleaving",
abstract = "This chapter examines the interleaving relation between persistence modules, and the associated interleaving metric. Interleavings are approximate isomorphisms, and in the first instance may be defined by a pair of {\textquoteleft}shifted{\textquoteright} homomorphisms between the two persistence modules being compared. More abstractly, an interleaving can be thought of as a solution to a functor extension problem. The Interpolation Lemma is the main result of this chapter: it asserts that a pair of interleaved persistence modules can be interpolated by a 1-Lipschitz 1-parameter family. We give three different explicit constructions of the interpolation; two of them are the left and right Kan extensions (in the functor extension point of view), while the third mediates between the two.",
keywords = "Functor Extension, Homology Module, Interpolation Parameter, Persistence Diagram, Persistent Homology",
author = "Fr{\'e}d{\'e}ric Chazal and \{de Silva\}, Vin and Marc Glisse and Steve Oudot",
note = "Publisher Copyright: {\textcopyright} 2016, The Author(s).",
year = "2016",
month = jan,
day = "1",
doi = "10.1007/978-3-319-42545-0\_4",
language = "English",
series = "SpringerBriefs in Mathematics",
publisher = "Springer Science and Business Media B.V.",
pages = "67--80",
booktitle = "SpringerBriefs in Mathematics",
}