Sparse handlebody decompositions and non-finiteness of g₃=0

2020/11/16 by Adiprasito, Karim, Benedetti, Bruno
#20F05 #52B05 #57Q15 #57R05 #57R65 #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2011.08312

Abstract

We prove that a PL manifold admits a handle decomposition into handles of index ≤ k if and only if M is k-stacked, i.e., it admits a PL triangulation in which all (d-k-1)-faces are on ∂ M. We use this to solve a problem posed in 2008 by Kalai: In any dimension higher than four, there are infinitely many homology-spheres with g₃ =0.

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