Disk surgery and the primitive disk complexes of the 3-sphere

2018/12/26 by Sangbum Cho, Cho, Sangbum, Yuya Koda +3
Mathematics · #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Advanced Combinatorial Mathematics

paper · pdf · doi:10.48550/arxiv.1812.10241

Abstract

Given a genus-g Heegaard splitting of the 3-sphere with g ≥ 3, we show that the primitive disk complex for the splitting is not weakly closed under disk surgery operation. That is, there exist two primitive disks in one of the handlebodies of the splitting such that any disk surgery on one along the other one yields no primitive disks.

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