--- _id: '3575' abstract: - lang: eng 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. alternative_title: - London Mathematical Society Lecture Note author: - first_name: Herbert full_name: Herbert Edelsbrunner id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: John full_name: Harer, John last_name: Harer citation: ama: 'Edelsbrunner H, Harer J. Jacobi sets of multiple Morse functions. In: Foundations of Computational Mathematics. Vol 312. Springer; 2004:37-57. doi:10.1017/CBO9781139106962.003' apa: Edelsbrunner, H., & Harer, J. (2004). Jacobi sets of multiple Morse functions. In Foundations of Computational Mathematics (Vol. 312, pp. 37–57). Springer. https://doi.org/10.1017/CBO9781139106962.003 chicago: Edelsbrunner, Herbert, and John Harer. “Jacobi Sets of Multiple Morse Functions.” In Foundations of Computational Mathematics, 312:37–57. Springer, 2004. https://doi.org/10.1017/CBO9781139106962.003. ieee: H. Edelsbrunner and J. Harer, “Jacobi sets of multiple Morse functions,” in Foundations of Computational Mathematics, vol. 312, Springer, 2004, pp. 37–57. 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.' mla: Edelsbrunner, Herbert, and John Harer. “Jacobi Sets of Multiple Morse Functions.” Foundations of Computational Mathematics, vol. 312, Springer, 2004, pp. 37–57, doi:10.1017/CBO9781139106962.003. short: H. Edelsbrunner, J. Harer, in:, Foundations of Computational Mathematics, Springer, 2004, pp. 37–57. date_created: 2018-12-11T12:04:02Z date_published: 2004-01-01T00:00:00Z date_updated: 2021-01-12T07:44:24Z day: '01' doi: 10.1017/CBO9781139106962.003 extern: 1 intvolume: ' 312' month: '01' page: 37 - 57 publication: Foundations of Computational Mathematics publication_status: published publisher: Springer publist_id: '2810' quality_controlled: 0 status: public title: Jacobi sets of multiple Morse functions type: book_chapter volume: 312 year: '2004' ...