Grid movies

Matthew Graham*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


We present a grid diagram analogue of Carter, Rieger and Saito's smooth movie theorem. Specifically, we give definitions for grid movies, grid movie isotopies and present a definition of grid planar isotopy as a particular subset of the grid diagram moves: stabilization, destabilization and commutation. We show that grid planar isotopy classes are in one-to-one correspondence with smooth planar isotopy classes by using a new planar grid algorithm that takes a smooth knot diagram to a grid diagram. We then present generalizations of both the smooth and grid movie theorems that apply to surfaces with boundary.

Original languageEnglish (US)
Article number1450038
JournalJournal of Knot Theory and its Ramifications
Issue number8
StatePublished - Jan 1 2014


  • grid diagrams
  • knot floer homology
  • Movies
  • planar isotopy

ASJC Scopus subject areas

  • Algebra and Number Theory

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