- M. Adamaszek and H. Adams. The Vietoris--Rips complexes of a circle. Pacific Journal of Mathematics, 290:1--40, 2017.Google ScholarCross Ref
- M. Adamaszek, H. Adams, F. Frick, C. Peterson, and C. Previte-Johnson. Nerve complexes of circular arcs. Discrete & Computational Geometry, 56(2):251--273, 2016. Google ScholarDigital Library
- M. Adamaszek, F. Frick, and A. Vakili. On homotopy types of Euclidean Rips complexes. Accepted by Discrete & Computational Geometry, arxiv/1602.04131, 2016. Google ScholarDigital Library
- K. Borsuk. On the imbedding of systems of compacta in simplicial complexes. Fundamenta Mathematicae, 35(1):217--234, 1948.Google ScholarCross Ref
- P. Bubenik, P. T. Kim, et al. A statistical approach to persistent homology. Homology, Homotopy and Applications, 9(2):337--362, 2007.Google ScholarCross Ref
- G. Carlsson. Topology and data. Bull. AMS, 46(2):255--308, 2009.Google ScholarCross Ref
- E. Chambers and Y. Wang. Measuring similarity between curves on 2-manifolds via homotopy area. In Proc. 29th Annual ACM Symposium on Computational Geometry, pages 425--434, 2013. Google ScholarDigital Library
- E. W. Chambers, G. R. Chambers, A. de Mesmay, T. Ophelders, and R. Rotman. Monotone contractions of the boundary of the disc. arXiv preprint arXiv:1704.06175, 2017.Google Scholar
- E. W. Chambers, A. de Mesmay, and T. Ophelders. Dagstuhl working group result, in prepration.Google Scholar
- E. W. Chambers, V. De Silva, J. Erickson, and R. Ghrist. Vietoris-Rips complexes of planar point sets. Discrete & Computational Geometry, 44:75--90, 2010. Google ScholarDigital Library
- E. W. Chambers and D. Letscher. On the height of a homotopy. In CCCG, volume 9, pages 103--106, 2009.Google Scholar
- J. M. Chan, G. Carlsson, and R. Rabadan. Topology of viral evolution. Proceedings of the National Academy of Sciences, 110(46):18566--18571, 2013.Google ScholarCross Ref
- T. K. Dey, J. Sun, and Y. Wang. Approximating loops in a shortest homology basis from point data. In Proceedings of the twenty-sixth annual symposium on Computational geometry, pages 166--175. ACM, 2010. Google ScholarDigital Library
- H. Edelsbrunner and J. Harer. Persistent homology - a survey. Contemporary Mathematics, 453:257, 2008.Google ScholarCross Ref
- H. Edelsbrunner and J. Harer. Computational Topology: An Introduction. AMS, 2010.Google Scholar
- H. Edelsbrunner, D. Letscher, and A. J. Zomorodian. Topological persistence and simplification. Discrete and Computational Geometry, 28:511--533, 2002. Google ScholarDigital Library
- E. Gasparovic, M. Gommel, E. Purvine, R. Sazdanovic, B.Wang, Y.Wang, and L. Ziegelmeier. Complete characterization of the 1-dimensional intrinsic ?Cech persistence diagrams for metric graphs. Preprint, arxiv/1702.07379, 2016.Google Scholar
- R. Ghrist. Barcodes: The persistent topology of data. Bull. AMS, 45:61--75, 2008.Google ScholarCross Ref
- R. W. Ghrist. Elementary Applied Topology. Createspace, 2014.Google Scholar
- J.-C. Hausmann. On the Vietoris-Rips complexes and a cohomology theory for metric spaces. Annals of Mathematics Studies, 138:175--188, 1995.Google Scholar
- E. Munch. A user's guide to topological data analysis. Journal of Learning Analytics, 4(2):47--61, 2017.Google ScholarCross Ref
- X. Zhu. Persistent homology: An introduction and a new text representation for natural language processing. In IJCAI, pages 1953--1959, 2013. ACM Google ScholarDigital Library
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