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Title: A lower bound on critical points of the electric potential of a knot
Consider a knot [Formula: see text] in [Formula: see text] with charge uniformly distributed on it. From the standpoint of both physics and knot theory, it is natural to try to understand the critical points of the potential and their behavior. We show the number of critical points of the potential is at least [Formula: see text], where [Formula: see text] is the tunnel number, defined as the smallest number of arcs one must add to [Formula: see text] such that its complement is a handlebody. The result is proven using Morse theory and stable manifold theory.  more » « less
Award ID(s):
1645643
PAR ID:
10286412
Author(s) / Creator(s):
Date Published:
Journal Name:
Journal of Knot Theory and Its Ramifications
Volume:
30
Issue:
04
ISSN:
0218-2165
Page Range / eLocation ID:
2150026
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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