@InProceedings{kim_et_al:LIPIcs.SoCG.2020.54, author = {Kim, Jisu and Shin, Jaehyeok and Chazal, Fr\'{e}d\'{e}ric and Rinaldo, Alessandro and Wasserman, Larry}, title = {{Homotopy Reconstruction via the Cech Complex and the Vietoris-Rips Complex}}, booktitle = {36th International Symposium on Computational Geometry (SoCG 2020)}, pages = {54:1--54:19}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-143-6}, ISSN = {1868-8969}, year = {2020}, volume = {164}, editor = {Cabello, Sergio and Chen, Danny Z.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2020.54}, URN = {urn:nbn:de:0030-drops-122129}, doi = {10.4230/LIPIcs.SoCG.2020.54}, annote = {Keywords: Computational topology, Homotopy reconstruction, Homotopy Equivalence, Vietoris-Rips complex, \v{C}ech complex, Reach, \mu-reach, Nerve Theorem, Offset, Double offset, Consistency} }