One way of visualizing and/or presenting higher dimensional bordisms/tangles/knots is as a sequence of pre-images of a sequence of values of a suitable Morse function. If one thinks of the Morse function here as assigning a “time”-cordinate to the bordism/tangle/knot then each of these pre-images is like a frame of a movie (Carter-Saito 93).

References

The term was introduced, in the context of surface knots in:

Scott Carter, Masahico Saito, Reidemeister moves for surface isotopies and their interpretations as moves to movies, Journal of Knot Theory and Its RamificationsVol. 02, No. 03, pp. 251-284 (1993) (doi:10.1142/S0218216593000167)

Review:

Carlo Collari, Chapter 2, Section 1.2 in: The Functoriality of Khovanov Homology and the Monodromy of Knots, 2013 (pdf, pdf)

Created on January 31, 2021 at 03:59:01.
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