Herbert Abels
Stephan Holz
1993
Higher generation by subgroups
Journal of Algebra
160
2
310–341
10.1006/jabr.1993.1190
MichałAdamaszek
Henry Adams
2017
The Vietoris–Rips complexes of a circle
Pacific Journal of Mathematics
290
1–40
10.1515/crll.1999.035
MichałAdamaszek
Henry Adams
Florian Frick
2018
Metric reconstruction via optimal transport
SIAM Journal on Applied Algebra and Geometry
2
4
597–619
10.1137/17M1148025
MichałAdamaszek
Henry Adams
Ellen Gasparovic
Maria Gommel
Emilie Purvine
Radmila Sazdanovic
Bei Wang
Yusu Wang
Lori Ziegelmeier
2018
Vietoris–Rips and Čech complexes of metric gluings
Proceedings of the 34th International Symposium on Computational Geometry
3:1–3:15
10.4230/LIPIcs.SoCG.2018.3
MichałAdamaszek
Henry Adams
Ellen Gasparovic
Maria Gommel
Emilie Purvine
Radmila Sazdanovic
Bei Wang
Yusu Wang
Lori Ziegelmeier
2020
On homotopy types of Vietoris–Rips complexes of metric gluings
Journal of Applied and Computational Topology
10.1007/s41468-020-00054-y
Henry Adams
Joshua Mirth
2019
Metric Thickenings of Euclidean Submanifolds
Topology and its Applications
254
69–84
10.1016/j.topol.2018.12.014
Martin R Bridson
André Haefliger
2011
Metric spaces of non-positive curvature
319
Springer Science & Business Media
10.1007/978-3-662-12494-9
Gunnar Carlsson
Benjamin Filippenko
2020
Persistent homology of the sum metric
Journal of Pure and Applied Algebra
224
5
106244
10.1016/j.jpaa.2019.106244
Wojciech Chachólski
Alvin Jin
Martina Scolamiero
Francesca Tombari
2020
Homotopical decompositions of simplicial and Vietoris Rips complexes
arXiv preprint arXiv:2002.03409
Frédéric Chazal
Vin De Silva
Steve Oudot
2014
Persistence stability for geometric complexes
Geometriae Dedicata
173
1
193–214
10.1007/s10711-013-9937-z
Clifford H Dowker
1952
Homology groups of relations
Annals of mathematics
84–95
10.2307/1969768
Clifford H Dowker
1952
Topology of metric complexes
American Journal of Mathematics
74
3
555–577
10.2307/2372262
David A Edwards
2011
On the Kantorovich–Rubinstein theorem
Expositiones Mathematicae
29
4
387–398
10.1016/j.exmath.2011.06.005
Tobias Fritz
Paolo Perrone
2019
A probability monad as the colimit of spaces of finite samples
Theory and Applications of Categories
34
7
170–220
Hitesh Gakhar
Jose A Perea
2019
Künneth Formulae in Persistent Homology
arXiv preprint arXiv:1910.05656
Ellen Gasparovic
Maria Gommel
Emilie Purvine
Radmila Sazdanovic
Bei Wang
Yusu Wang
Lori Ziegelmeier
2018
A complete characterization of the one-dimensional intrinsic Čech persistence diagrams for metric graphs
Research in Computational Topology
Springer
33–56
10.1007/s11083-015-9379-3
Ellen Gasparovic
Maria Gommel
Emilie Purvine
Radmila Sazdanovic
Bei Wang
Yusu Wang
Lori Ziegelmeier
2018
The Relationship Between the Intrinsic Čech and Persistence Distortion Distances for Metric Graphs
arXiv preprint arXiv:1812.05282
Manin Gelfand
1988
Methods of Homological Algebra
Springer
10.1007/978-3-662-12492-5
Hatcher, Allen
2001
Algebraic Topology
Cambridge University Press
10.1017/S0013091503214620
Hans G Kellerer
1984
Duality theorems for marginal problems
Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete
67
4
399–432
10.1007/BF00532047
Hans G Kellerer
1985
Duality theorems and probability metrics
Proceedings of the Seventh Conference on Probability theory, Braşov, Romania
211–220
Dmitry N Kozlov
2008
Combinatorial Algebraic Topology
Algorithms and Computation in Mathematics
21
Springer
10.1007/978-3-540-71962-5_3
F William Lawvere
1973
Metric spaces, generalized logic, and closed categories
Rendiconti del seminario matématico e fisico di Milano
43
1
135–166
10.1007/BF02924844
Michael Lesnick
Raúl Rabadán
Daniel IS Rosenbloom
2020
Quantifying genetic innovation: Mathematical foundations for the topological study of reticulate evolution
SIAM Journal on Applied Algebra and Geometry
4
1
141–184
10.1137/18M118150X
Sunhyuk Lim
Facundo Memoli
Osman Berat Okutan
2020
Vietoris–Rips persistent homology, injective metric spaces, and the filling radius
arXiv preprint arXiv:2001.07588
Ernest G Manes
2012
Algebraic theories
26
Springer Science & Business Media
10.1002/zamm.19780580331
Ivan Marin
2017
Measure theory and classifying spaces
arXiv preprint arXiv:1702.01889
Ivan Marin
2017
Simplicial random variables
arXiv preprint arXiv:1703.03987
James R Munkres
1975
Topology: A First Course
Prentice-Hall
Paolo Perrone
2018
Categorical Probability and Stochastic Dominance in Metric Spaces
University of Leipzig
Emily Riehl
2016
Category Theory in Context
Aurora: Dover Modern Math Originals
Dover
Walter Rudin
1976
Principles of Mathematical Analysis
3d ed
International series in pure and applied mathematics
McGraw-Hill
New York
10.1017/S0013091500008889
Cédric Villani
2003
Topics in optimal transportation
Graduate Studies in Mathematics
58
American Mathematical Society
10.1090/gsm/058/05
Cédric Villani
2008
Optimal Transport, Old and New
Springer
10.1007/978-3-540-71050-9
Žiga Virk
2018
1-dimensional intrinsic persistence of geodesic spaces
Journal of Topology and Analysis
1–39
10.1142/S1793525319500444
Žiga Virk
2019
Rips complexes as nerves and a functorial Dowker-nerve diagram
arXiv preprint arXiv:1906.04028
Matthew C. B. Zaremsky
2018
Bestvina–Brady discrete Morse theory and Vietoris–Rips complexes
arXiv preprint arXiv:1812.10976