Alexander numbering of knotted surface diagrams

Carter, J.; Kamada, Seiichi; Saito, Masahico

doi:10.1090/S0002-9939-00-05479-4

Alexander numbering of knotted surface diagrams
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by J. Scott Carter, Seiichi Kamada and Masahico Saito PDF

Proc. Amer. Math. Soc. 128 (2000), 3761-3771 Request permission

Abstract:

A generic projection of a knotted oriented surface in 4-space divides $3$-space into regions. The number of times (counted with sign) that a path from infinity to a given region intersects the projected surface is called the Alexander numbering of the region. The Alexander numbering is extended to branch and triple points of the projections. A formula that relates these indices is presented.

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