A characterization of normal 3-pseudomanifolds with at most two singularities

Characterizing face-number-related invariants of a given class simplicial complexes has been central topic in combinatorial topology. In this regard, one the well-known is g2. Let K be normal 3-pseudomanifold such that g2(K)≤g2(lk(v))+9 for some vertex v K. Suppose either only singularity or two singularities (at least) which an RP2-singularity. We prove obtained from boundary 4-simplices by sequence operations types connected sums, bistellar 1-moves, edge contractions, expansions, foldings, and foldings. case singularity, |K| handlebody with its coned off. Further, we above upper bound sharp 3-pseudomanifolds.