Tohoku Mathematical Journal
2013
September
SECOND SERIES VOL. 65, NO. 3

Tohoku Math. J.
65 (2013), 427-440

Title MEASURE OF A 2-COMPONENT LINK

Author Jun O'Hara

(Received October 24, 2011, revised February 5, 2013)
Abstract. A two-component link produces a torus as the product of the component knots in a two-point configuration space of a three-sphere. This space can be identified with a cotangent bundle and also with an indefinite Grassmannian. We show that the integration of the absolute value of the canonical symplectic form is equal to the area of the torus with respect to the pseudo-Riemannian structure, and that it attains the minimum only at the “best” Hopf links.

Mathematics Subject Classification. Primary 57M25; Secondary 53A30.
Key words and phrases. Energy, link, symplectic measure, Möbius geometry, pseudo-Riemannian geometry.

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