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2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory internal-categories k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeApr 3rd 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to today's * [[Gunnar Carlsson]], _Persistent Homology and Applied Homotopy Theory_, in: [[Handbook of Homotopy Theory]], CRC Press, 2019 ([arXiv:2004.00738](https://arxiv.org/abs/2004.00738)) <a href="https://ncatlab.org/nlab/revision/diff/persistent+homology/25">diff</a>, <a href="https://ncatlab.org/nlab/revision/persistent+homology/25">v25</a>, <a href="https://ncatlab.org/nlab/show/persistent+homology">current</a>

   added pointer to today’s

   • Gunnar Carlsson, Persistent Homology and Applied Homotopy Theory, in: Handbook of Homotopy Theory, CRC Press, 2019 (arXiv:2004.00738)

   diff, v25, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeSep 11th 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to today's * Matteo Biagetti, Alex Cole, [[Gary Shiu]], _The Persistence of Large Scale Structures I: Primordial non-Gaussianity_ ([arXiv:2009.04819](https://arxiv.org/abs/2009.04819)) <a href="https://ncatlab.org/nlab/revision/diff/persistent+homology/26">diff</a>, <a href="https://ncatlab.org/nlab/revision/persistent+homology/26">v26</a>, <a href="https://ncatlab.org/nlab/show/persistent+homology">current</a>

   added pointer to today’s

   • Matteo Biagetti, Alex Cole, Gary Shiu, The Persistence of Large Scale Structures I: Primordial non-Gaussianity (arXiv:2009.04819)

   diff, v26, current

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeMay 20th 2022
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have re-written the Idea-section from scratch and expanded a fair bit ([here](https://ncatlab.org/nlab/show/persistent+homology#Idea)). (There used to be a puny such section, and then something like a second attempt at it further below but also not much more informative. I have taken the liberty of deleting both. I believe what I have written now subsumes whatever worthwhile there was before.) <a href="https://ncatlab.org/nlab/revision/diff/persistent+homology/34">diff</a>, <a href="https://ncatlab.org/nlab/revision/persistent+homology/34">v34</a>, <a href="https://ncatlab.org/nlab/show/persistent+homology">current</a>

   I have re-written the Idea-section from scratch and expanded a fair bit (here).

   (There used to be a puny such section, and then something like a second attempt at it further below but also not much more informative. I have taken the liberty of deleting both. I believe what I have written now subsumes whatever worthwhile there was before.)

   diff, v34, current

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeJun 13th 2022
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * [[Stefan Huber]], *Persistent Homology in Data Science* In: *Data Science – Analytics and Applications* Springer (2021) $[$[doi:10.1007/978-3-658-32182-6_13](https://doi.org/10.1007/978-3-658-32182-6_13), [pdf](https://www.sthu.org/research/publications/files/Hub20.pdf)$]$ <a href="https://ncatlab.org/nlab/revision/diff/persistent+homology/37">diff</a>, <a href="https://ncatlab.org/nlab/revision/persistent+homology/37">v37</a>, <a href="https://ncatlab.org/nlab/show/persistent+homology">current</a>

   added pointer to:

   • Stefan Huber, Persistent Homology in Data Science In: Data Science – Analytics and Applications Springer (2021) $[$doi:10.1007/978-3-658-32182-6_13, pdf$]$

   diff, v37, current

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeAug 4th 2023
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to today's * [[Wojciech Chachólski]], Alessandro De Gregorio, Nicola Quercioli, Francesca Tombari: *Symmetries of data sets and functoriality of persistent homology*, Theory and Applications of Categories **39** 23 (2023) 667-686 &lbrack;[tac:39/23](http://www.tac.mta.ca/tac/volumes/39/23/39-23abs.html)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/persistent+homology/41">diff</a>, <a href="https://ncatlab.org/nlab/revision/persistent+homology/41">v41</a>, <a href="https://ncatlab.org/nlab/show/persistent+homology">current</a>

   added pointer to today’s

   • Wojciech Chachólski, Alessandro De Gregorio, Nicola Quercioli, Francesca Tombari: Symmetries of data sets and functoriality of persistent homology, Theory and Applications of Categories 39 23 (2023) 667-686 [tac:39/23]

   diff, v41, current