References

  1. Herbert Abels & Stephan Holz (1993): Higher generation by subgroups. Journal of Algebra 160(2), pp. 310–341, doi:10.1006/jabr.1993.1190.
  2. 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.
  3. 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.
  4. 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.
  5. 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.
  6. 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.
  7. 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.
  8. 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.
  9. Wojciech Chachólski, Alvin Jin, Martina Scolamiero & Francesca Tombari (2020): Homotopical decompositions of simplicial and Vietoris Rips complexes. arXiv preprint arXiv:2002.03409.
  10. 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.
  11. Clifford H Dowker (1952): Homology groups of relations. Annals of mathematics, pp. 84–95, doi:10.2307/1969768.
  12. Clifford H Dowker (1952): Topology of metric complexes. American Journal of Mathematics 74(3), pp. 555–577, doi:10.2307/2372262.
  13. David A Edwards (2011): On the Kantorovich–Rubinstein theorem. Expositiones Mathematicae 29(4), pp. 387–398, doi:10.1016/j.exmath.2011.06.005.
  14. 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.
  15. Hitesh Gakhar & Jose A Perea (2019): Künneth Formulae in Persistent Homology. arXiv preprint arXiv:1910.05656.
  16. 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.
  17. 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.
  18. Manin Gelfand (1988): Methods of Homological Algebra. Springer, doi:10.1007/978-3-662-12492-5.
  19. Hatcher, Allen (2001): Algebraic Topology. Cambridge University Press, doi:10.1017/S0013091503214620.
  20. Hans G Kellerer (1984): Duality theorems for marginal problems. Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete 67(4), pp. 399–432, doi:10.1007/BF00532047.
  21. Hans G Kellerer (1985): Duality theorems and probability metrics. In: Proceedings of the Seventh Conference on Probability theory, Braşov, Romania, pp. 211–220.
  22. Dmitry N Kozlov (2008): Combinatorial Algebraic Topology. Algorithms and Computation in Mathematics 21. Springer, doi:10.1007/978-3-540-71962-5_3.
  23. 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.
  24. 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.
  25. Sunhyuk Lim, Facundo Memoli & Osman Berat Okutan (2020): Vietoris–Rips persistent homology, injective metric spaces, and the filling radius. arXiv preprint arXiv:2001.07588.
  26. Ernest G Manes (2012): Algebraic theories 26. Springer Science & Business Media, doi:10.1002/zamm.19780580331.
  27. Ivan Marin (2017): Measure theory and classifying spaces. arXiv preprint arXiv:1702.01889.
  28. Ivan Marin (2017): Simplicial random variables. arXiv preprint arXiv:1703.03987.
  29. James R Munkres (1975): Topology: A First Course. Prentice-Hall.
  30. Paolo Perrone (2018): Categorical Probability and Stochastic Dominance in Metric Spaces. University of Leipzig.
  31. Emily Riehl (2016): Category Theory in Context. Aurora: Dover Modern Math Originals. Dover.
  32. 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.
  33. Cédric Villani (2003): Topics in optimal transportation. Graduate Studies in Mathematics 58. American Mathematical Society, doi:10.1090/gsm/058/05.
  34. Cédric Villani (2008): Optimal Transport, Old and New. Springer, doi:10.1007/978-3-540-71050-9.
  35. Žiga Virk (2018): 1-dimensional intrinsic persistence of geodesic spaces. Journal of Topology and Analysis, pp. 1–39, doi:10.1142/S1793525319500444.
  36. Žiga Virk (2019): Rips complexes as nerves and a functorial Dowker-nerve diagram. arXiv preprint arXiv:1906.04028.
  37. Matthew C. B. Zaremsky (2018): Bestvina–Brady discrete Morse theory and Vietoris–Rips complexes. arXiv preprint arXiv:1812.10976.

Comments and questions to: eptcs@eptcs.org
For website issues: webmaster@eptcs.org