Yoshikawa moves on marked graphs via Roseman's theorem

2017/01/25 by Chterental, Oleg
#FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1701.07170

Abstract

Yoshikawa [Yo] conjectured that a certain set of moves on marked graph diagrams generates the isotopy relation for surface links in \mathbb R⁴, and this was proved by Swenton [S] and Kearton and Kurlin [KK]. In this paper, we find another proof of this fact for the case of 2-links (surface links with spherical components). The proof involves a version of Roseman's theorem [R] for branch-free broken surface diagrams of 2-links and a construction of marked graphs from branch-free broken surface diagrams.

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