---
_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'
...