A characterization of normal 3-pseudomanifolds with g₂≤4

2022/02/14 by Basak, Biplab, Gupta, Raju Kumar
#57Q05 #57Q15 #57Q25 #Combinatorics (math.CO) #FOS: Mathematics #General Topology (math.GN) #Primary 05E45 #secondary 52B05

paper · doi:10.48550/arxiv.2202.06638

Abstract

We characterize normal 3-pseudomanifolds with g₂≤4. We know that if a 3-pseudomanifold with g₂≤4 does not have any singular vertices then it is a 3-sphere. We first prove that a normal 3-pseudomanifold with g₂≤4 has at most two singular vertices. Then we prove that a normal 3-pseudomanifold with g₂ ≤ 4, which is not a 3-sphere is obtained from some boundary of 4-simplices by a sequence of operations connected sum, edge expansion and an edge folding. In addition, by using [17], we re-framed the characterization of normal 3-pseudomanifolds with g₂≤ 9, when it has no singular vertices.

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