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Generalized Gauss maps and integrals for three-component links: Toward higher helicities for magnetic fields and fluid flows
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View: Figures


Image of FIG. 1.
FIG. 1.

The Grassmann map (x, y, z) ↦ G(x, y, z).

Image of FIG. 2.
FIG. 2.

The link L in S 3.

Image of FIG. 3.
FIG. 3.

The base link L pqr for p = 5, q = 3, r = −2.

Image of FIG. 4.
FIG. 4.

The delta move

Image of FIG. 5.
FIG. 5.

A negative triple point appears.

Image of FIG. 6.
FIG. 6.

Pontryagin link for the base map f pqr .

Image of FIG. 7.
FIG. 7.

Toral diagrams of framed links in T3.

Image of FIG. 8.
FIG. 8.

Using saddles to eliminate crossings.

Image of FIG. 9.
FIG. 9.

The saddle bordism.

Image of FIG. 10.
FIG. 10.

Depths of components in the diagram.

Image of FIG. 11.
FIG. 11.

The deformation retraction Conf3 S 3V.

Image of FIG. 12.
FIG. 12.

Pure imaginary quaternion 3-space.

Image of FIG. 13.
FIG. 13.

The standard open book in .

Image of FIG. 14.
FIG. 14.

A generic link.

Image of FIG. 15.
FIG. 15.

Page vectors.

Image of FIG. 16.
FIG. 16.

Local pictures of a bicycle and its corresponding icycle.

Image of FIG. 17.
FIG. 17.

Bicycle arising from a clasp.

Image of FIG. 18.
FIG. 18.

A generic link and its icycles.

Image of FIG. 19.
FIG. 19.

A double crossing change.

Image of FIG. 20.
FIG. 20.

The smoothed link L 0  =  PQZ.

Image of FIG. 21.
FIG. 21.

A simple double crossing change.

Image of FIG. 22.
FIG. 22.

A generic link L representing L pqr .

Image of FIG. 23.
FIG. 23.

Another view of the delta move.

Image of FIG. 24.
FIG. 24.

Fundamental solution of the scalar Laplacian on S 1×S 1.

Image of FIG. 25.
FIG. 25.

Using saddles to transfer twists.

Image of FIG. 26.
FIG. 26.

Using saddles to replace vertical winding by vertical circles.

Image of FIG. 27.
FIG. 27.

Using saddles to gather the vertical circles.

Image of FIG. 28.
FIG. 28.

k is regular.

Image of FIG. 29.
FIG. 29.

Orientation of the Pontryagin link.

Image of FIG. 30.
FIG. 30.

The linking of P = X −+Y +− and Z.

Image of FIG. 31.
FIG. 31.

Borromean rings.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Generalized Gauss maps and integrals for three-component links: Toward higher helicities for magnetic fields and fluid flows