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Title: Twist number and the alternating volume of knots
It was previously shown by the first author that every knot in [Formula: see text] is ambient isotopic to one component of a two-component, alternating, hyperbolic link. In this paper, we define the alternating volume of a knot [Formula: see text] to be the minimum volume of any link [Formula: see text] in a natural class of alternating, hyperbolic links such that [Formula: see text] is ambient isotopic to a component of [Formula: see text]. Our main result shows that the alternating volume of a knot is coarsely equivalent to the twist number of a knot.  more » « less
Award ID(s):
1821254
PAR ID:
10161375
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
Journal of Knot Theory and Its Ramifications
Volume:
28
Issue:
01
ISSN:
0218-2165
Page Range / eLocation ID:
1950016
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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