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On an algebraic description of marked braid diagrams for surface-links
by
Michal Jablonowski
University of Gdansk
We will discuss a method for presentation of knotted surfaces in the four space by investigating a monoid corresponding to the braid form of marked graph diagrams, where algebraic relations on words will be derived from the topological Yoshikawa moves (which sufficiency was proved by Swenton, Kearton and Kurlin). This method start with the use of transverse cross-sections (by Fox and Milnor) and producing a four-valent graph from the hyperbolic splitting (introduced by Lomonaco, Kawauchi, Shibuya, Suzuki and Kamada) of a knotted surface. In a quest to resolve linearity problem for this monoid, we will show that if it is defined on at least two or at least three strands, then its two or respectively three dimensional representations are not faithful.
Date received: November 11, 2016
Copyright © 2016 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cbnq-22.