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The homotopy interleaving distance, a distance between persistent spaces, was introduced by Blumberg and Lesnick and shown to be universal, in the sense that it is the largest homotopy-invariant distance for which sublevel-set filtrations of close-by real-valued functions are close-by. There are other ways of constructing homotopy-invariant distances, but not much is known about the relationships between these choices. We show that other natural distances differ from the homotopy interleaving distance in at most a multiplicative constant, and prove versions of the persistent Whitehead theorem, a conjecture of Blumberg and Lesnick that relates morphisms that induce interleavings in persistent homotopy groups to stronger homotopy-invariant notions of interleaving.
Lanari, Edoardo 1 ; Scoccola, Luis 2
@article{10_2140_agt_2023_23_803,
author = {Lanari, Edoardo and Scoccola, Luis},
title = {Rectification of interleavings and a persistent {Whitehead} theorem},
journal = {Algebraic and Geometric Topology},
pages = {803--832},
publisher = {mathdoc},
volume = {23},
number = {2},
year = {2023},
doi = {10.2140/agt.2023.23.803},
url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2023.23.803/}
}
TY - JOUR AU - Lanari, Edoardo AU - Scoccola, Luis TI - Rectification of interleavings and a persistent Whitehead theorem JO - Algebraic and Geometric Topology PY - 2023 SP - 803 EP - 832 VL - 23 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.2140/agt.2023.23.803/ DO - 10.2140/agt.2023.23.803 ID - 10_2140_agt_2023_23_803 ER -
%0 Journal Article %A Lanari, Edoardo %A Scoccola, Luis %T Rectification of interleavings and a persistent Whitehead theorem %J Algebraic and Geometric Topology %D 2023 %P 803-832 %V 23 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.2140/agt.2023.23.803/ %R 10.2140/agt.2023.23.803 %F 10_2140_agt_2023_23_803
Lanari, Edoardo; Scoccola, Luis. Rectification of interleavings and a persistent Whitehead theorem. Algebraic and Geometric Topology, Tome 23 (2023) no. 2, pp. 803-832. doi: 10.2140/agt.2023.23.803
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