30 pages + 15 pages appendix, 19 figures, LaTeX; moved an appendix to arXiv:2108.09298, generalization of results to restricted extended persistence diagrams, added discussion of relations to interleaving distances of sheaves and of Reeb graphs, correction of a sign mistake in the proof of lemma 3.2 with additional details in appendix D, updated references, several minor edits
发表信息：
Journal of Applied and Computational Topology - ATMCS10 Special Issue (2024)
The extended persistence diagram is an invariant of piecewise linear functions, which is known to be stable under perturbations of functions with respect to the bottleneck distance as introduced by Cohen-Steiner, Edelsbrunner, and Harer. We address the question of universality, which asks for the largest possible stable distance on extended persistence diagrams, showing that a more discriminative variant of the bottleneck distance is universal. Our result applies more generally to settings where persistence diagrams are considered only up to a certain degree. We achieve our results by establishing a functorial construction and several characteristic properties of relative interlevel set homology, which mirror the classical Eilenberg--Steenrod axioms. Finally, we contrast the bottleneck distance with the interleaving distance of sheaves on the real line by showing that the latter is not intrinsic, let alone universal. This particular result has the further implication that the interleaving distance of Reeb graphs is not intrinsic either.
Death and extended persistence in computational algebraic topology
本文的主要目的是探索持久同调和扩展持久同调的思想，以及它们的稳定性定理，使用[Bubenik and Scott，2014; Cohen-Steiner，Edelsbrunner，and Harer，2007; and Cohen-Steiner，Edelsbrunner，and Harer，2009]以及其他来源的思想。第二个目的是探索非可定向曲面的同调（和上同调），以克莱因瓶为例。我们还使用的克莱因瓶作为一个例子的计算（扩展）持久的同源性，在整个文件中提到它。
A distance between maps via interleavings of relative Sullivan algebras
Shinshu University（信州大学）；Nippon Institute of Technology（日本工业大学）；Graduate School of Medicine, Science and Technology, Shinshu University（信州大学医学部理工学研究科）；Graduate School of Mathematics, Nagoya University（名古屋大学大学院数学研究科）；Faculty of Education, Kochi University（高知大学教育学部）
Computing extended persistent homology of radial distance filtrations of Euclidean shapes
Division of Applied Mathematics, Brown University（布朗大学应用数学系）；Research School of Physics, Australian National University（澳大利亚国立大学物理研究学院）；Mathematical Sciences Institute, Australian National University（澳大利亚国立大学数学科学研究所）
Complex Matching Distance and Stability for Minimal Projective Resolutions, with Applications to Persistence
Department of Mathematics, Faculty of Science, Shizuoka University（静冈大学理学部数学系）；Osaka Central Advanced Mathematical Institute（大阪中央高级数学研究所）；Department of Mathematics, Colorado State University（科罗拉多州立大学数学系）
