{"abstract":[{"text":"The Jacobi set of two Morse functions defined on a common - manifold is the set of critical points of the restrictions of one func- tion to the level sets of the other function. Equivalently, it is the set of points where the gradients of the functions are parallel. For a generic pair of Morse functions, the Jacobi set is a smoothly embed- ded 1-manifold. We give a polynomial-time algorithm that com- putes the piecewise linear analog of the Jacobi set for functions specified at the vertices of a triangulation, and we generalize all results to more than two but at most Morse functions.","lang":"eng"}],"doi":"10.1017/CBO9781139106962.003","year":"2004","author":[{"orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Herbert Edelsbrunner"},{"last_name":"Harer","first_name":"John","full_name":"Harer, John"}],"page":"37 - 57","type":"book_chapter","month":"01","publisher":"Springer","alternative_title":["London Mathematical Society Lecture Note"],"publist_id":"2810","quality_controlled":0,"title":"Jacobi sets of multiple Morse functions","intvolume":"       312","citation":{"ieee":"H. Edelsbrunner and J. Harer, “Jacobi sets of multiple Morse functions,” in <i>Foundations of Computational Mathematics</i>, vol. 312, Springer, 2004, pp. 37–57.","ama":"Edelsbrunner H, Harer J. Jacobi sets of multiple Morse functions. In: <i>Foundations of Computational Mathematics</i>. Vol 312. Springer; 2004:37-57. doi:<a href=\"https://doi.org/10.1017/CBO9781139106962.003\">10.1017/CBO9781139106962.003</a>","apa":"Edelsbrunner, H., &#38; Harer, J. (2004). Jacobi sets of multiple Morse functions. In <i>Foundations of Computational Mathematics</i> (Vol. 312, pp. 37–57). Springer. <a href=\"https://doi.org/10.1017/CBO9781139106962.003\">https://doi.org/10.1017/CBO9781139106962.003</a>","chicago":"Edelsbrunner, Herbert, and John Harer. “Jacobi Sets of Multiple Morse Functions.” In <i>Foundations of Computational Mathematics</i>, 312:37–57. Springer, 2004. <a href=\"https://doi.org/10.1017/CBO9781139106962.003\">https://doi.org/10.1017/CBO9781139106962.003</a>.","ista":"Edelsbrunner H, Harer J. 2004.Jacobi sets of multiple Morse functions. In: Foundations of Computational Mathematics. London Mathematical Society Lecture Note, vol. 312, 37–57.","short":"H. Edelsbrunner, J. Harer, in:, Foundations of Computational Mathematics, Springer, 2004, pp. 37–57.","mla":"Edelsbrunner, Herbert, and John Harer. “Jacobi Sets of Multiple Morse Functions.” <i>Foundations of Computational Mathematics</i>, vol. 312, Springer, 2004, pp. 37–57, doi:<a href=\"https://doi.org/10.1017/CBO9781139106962.003\">10.1017/CBO9781139106962.003</a>."},"date_created":"2018-12-11T12:04:02Z","status":"public","date_published":"2004-01-01T00:00:00Z","date_updated":"2021-01-12T07:44:24Z","day":"01","extern":1,"publication":"Foundations of Computational Mathematics","_id":"3575","publication_status":"published","volume":312}