The Grassmann map (x, y, z) ↦ G(x, y, z).
The link L in S 3.
The base link L pqr for p = 5, q = 3, r = −2.
The delta move
A negative triple point appears.
Pontryagin link for the base map f pqr .
Toral diagrams of framed links in T 3.
Using saddles to eliminate crossings.
The saddle bordism.
Depths of components in the diagram.
The deformation retraction Conf3 S 3 → V.
Pure imaginary quaternion 3-space.
The standard open book in .
A generic link.
Local pictures of a bicycle and its corresponding icycle.
Bicycle arising from a clasp.
A generic link and its icycles.
A double crossing change.
The smoothed link L 0 = P ∪ Q ∪ Z.
A simple double crossing change.
A generic link L representing L pqr .
Another view of the delta move.
Fundamental solution of the scalar Laplacian on S 1×S 1.
Using saddles to transfer twists.
Using saddles to replace vertical winding by vertical circles.
Using saddles to gather the vertical circles.
k is regular.
Orientation of the Pontryagin link.
The linking of P = X −+ ∪ Y +− and Z.
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