{"quality_controlled":0,"volume":30,"year":"2003","acknowledgement":"Partially supported by ARO under Grant DAAG55-98-1-0177, NSF under Grants CCR-97-12088, EIA-9972879 and CCR-00-86013.","intvolume":"        30","date_published":"2003-07-01T00:00:00Z","extern":1,"author":[{"first_name":"Herbert","last_name":"Edelsbrunner","full_name":"Herbert Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833"},{"full_name":"Harer, John","last_name":"Harer","first_name":"John"},{"last_name":"Zomorodian","full_name":"Zomorodian, Afra","first_name":"Afra"}],"abstract":[{"text":"We present algorithms for constructing a hierarchy of increasingly coarse Morse-Smale complexes that decompose a piecewise linear 2-manifold. While these complexes are defined only in the smooth category, we extend the construction to the piecewise linearcategory by ensuring structural integrity and simulating differentiability. We then simplify Morse-Smale complexes by canceling pairs of critical points in order of increasing persistence.","lang":"eng"}],"publist_id":"2134","citation":{"chicago":"Edelsbrunner, Herbert, John Harer, and Afra Zomorodian. “Hierarchical Morse-Smale Complexes for Piecewise Linear 2-Manifolds.” <i>Discrete &#38; Computational Geometry</i>. Springer, 2003. <a href=\"https://doi.org/10.1007/s00454-003-2926-5\">https://doi.org/10.1007/s00454-003-2926-5</a>.","apa":"Edelsbrunner, H., Harer, J., &#38; Zomorodian, A. (2003). Hierarchical Morse-Smale complexes for piecewise linear 2-manifolds. <i>Discrete &#38; Computational Geometry</i>. Springer. <a href=\"https://doi.org/10.1007/s00454-003-2926-5\">https://doi.org/10.1007/s00454-003-2926-5</a>","mla":"Edelsbrunner, Herbert, et al. “Hierarchical Morse-Smale Complexes for Piecewise Linear 2-Manifolds.” <i>Discrete &#38; Computational Geometry</i>, vol. 30, no. 1, Springer, 2003, pp. 87–107, doi:<a href=\"https://doi.org/10.1007/s00454-003-2926-5\">10.1007/s00454-003-2926-5</a>.","short":"H. Edelsbrunner, J. Harer, A. Zomorodian, Discrete &#38; Computational Geometry 30 (2003) 87–107.","ista":"Edelsbrunner H, Harer J, Zomorodian A. 2003. Hierarchical Morse-Smale complexes for piecewise linear 2-manifolds. Discrete &#38; Computational Geometry. 30(1), 87–107.","ieee":"H. Edelsbrunner, J. Harer, and A. Zomorodian, “Hierarchical Morse-Smale complexes for piecewise linear 2-manifolds,” <i>Discrete &#38; Computational Geometry</i>, vol. 30, no. 1. Springer, pp. 87–107, 2003.","ama":"Edelsbrunner H, Harer J, Zomorodian A. Hierarchical Morse-Smale complexes for piecewise linear 2-manifolds. <i>Discrete &#38; Computational Geometry</i>. 2003;30(1):87-107. doi:<a href=\"https://doi.org/10.1007/s00454-003-2926-5\">10.1007/s00454-003-2926-5</a>"},"_id":"3993","type":"journal_article","date_created":"2018-12-11T12:06:19Z","issue":"1","publisher":"Springer","title":"Hierarchical Morse-Smale complexes for piecewise linear 2-manifolds","month":"07","date_updated":"2021-01-12T07:53:43Z","publication":"Discrete & Computational Geometry","publication_status":"published","day":"01","doi":"10.1007/s00454-003-2926-5","status":"public","page":"87 - 107"}