Primitive disk complexes for lens spaces

2012/06/27 by Sangbum Cho, Cho, Sangbum, Yuya Koda +1 · 1 citation
Mathematics · #57N10 #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:57N10

paper · pdf · doi:10.48550/arxiv.1206.6243

26 pages, 11 figures

arxiv created 2012/06/27 · arxiv updated 2012/06/28

Abstract

For a genus two Heegaard splitting of a lens space, the primitive disk complex is defined to be the full subcomplex of the disk complex for one of the handlebodies of the splitting spanned by all vertices of primitive disks. In this work, we describe the complete combinatorial structure of the primitive disk complex for the genus two Heegaard splitting of each lens space. In particular, we find all lens spaces whose primitive disk complexes are contractible.

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• Connected primitive disk complexes and genus two Goeritz groups of lens spaces

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