Herbert Abels & Stephan Holz (1993):
Higher generation by subgroups.
Journal of Algebra 160(2),
pp. 310–341,
doi:10.1006/jabr.1993.1190.
MichałAdamaszek & Henry Adams (2017):
The Vietoris–Rips complexes of a circle.
Pacific Journal of Mathematics 290,
pp. 1–40,
doi: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),
pp. 597–619,
doi: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,
pp. 3:1–3:15,
doi: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,
doi:10.1007/s41468-020-00054-y.
Henry Adams & Joshua Mirth (2019):
Metric Thickenings of Euclidean Submanifolds.
Topology and its Applications 254,
pp. 69–84,
doi:10.1016/j.topol.2018.12.014.
Martin R Bridson & André Haefliger (2011):
Metric spaces of non-positive curvature 319.
Springer Science & Business Media,
doi: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),
pp. 106244,
doi: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),
pp. 193–214,
doi:10.1007/s10711-013-9937-z.
Clifford H Dowker (1952):
Homology groups of relations.
Annals of mathematics,
pp. 84–95,
doi:10.2307/1969768.
Clifford H Dowker (1952):
Topology of metric complexes.
American Journal of Mathematics 74(3),
pp. 555–577,
doi:10.2307/2372262.
David A Edwards (2011):
On the Kantorovich–Rubinstein theorem.
Expositiones Mathematicae 29(4),
pp. 387–398,
doi: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),
pp. 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.
In: Research in Computational Topology.
Springer,
pp. 33–56,
doi: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.
Hatcher, Allen (2001):
Algebraic Topology.
Cambridge University Press,
doi:10.1017/S0013091503214620.
Hans G Kellerer (1984):
Duality theorems for marginal problems.
Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete 67(4),
pp. 399–432,
doi:10.1007/BF00532047.
Hans G Kellerer (1985):
Duality theorems and probability metrics.
In: Proceedings of the Seventh Conference on Probability theory, Braşov, Romania,
pp. 211–220.
Dmitry N Kozlov (2008):
Combinatorial Algebraic Topology.
Algorithms and Computation in Mathematics 21.
Springer,
doi: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),
pp. 135–166,
doi: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),
pp. 141–184,
doi: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,
doi: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 edition,
International series in pure and applied mathematics.
McGraw-Hill,
New York,
doi:10.1017/S0013091500008889.
Cédric Villani (2003):
Topics in optimal transportation.
Graduate Studies in Mathematics 58.
American Mathematical Society,
doi:10.1090/gsm/058/05.