ISSN:
1573-0530
Keywords:
57Q45
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Physics
Notes:
Abstract The elementary string interactions are the Reidemeister moves, birth/death, and fusion/fission. Such interactions have as their trace generically mapped surfaces, and these combine to form knotted surfaces in 4-space. The syzygies among these interactions are moves to such surfaces analogous to the Reidemeister moves for knots. ‘Movie’ parametrizations of these syzygies are given and interpreted in dimension 2+2. A Morse theoretic argument shows there are 15 such movie moves. These moves, with appropriate choices of crossing information, are sufficient to construct any isotopy of an embedded surface on which a height function has been specified. The first seven of the movie moves are parametrized versions of those given by Roseman. The remaining eight are moves of Δ-type. Amplitudes assigned to these interactions must satisfy relations that correspond to the movie moves. One such relation is a Zamolodchikov tetrahedral equation. We present some puzzles about the matrix formulations of these amplitudes.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00398826
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