Topological and combinatorial characterizations of normal 3-pseudomanifolds with g 2 ≤ 5

In recent years, characterizing normal pseudomanifolds with respect to small g 2 has become a very popular topic. For normal 3-pseudomanifolds with g 2 <= 4 and 3 -manifolds with g 2 <= 9, the topological and combinatorial characterizations are known. In this article, we characterize normal 3-pseudomanifolds with g 2 = 5. First, we show that a normal 3pseudomanifold with g 2 = 5 has no more than two singular vertices. Then, we show that a normal 3-pseudomanifold K with g 2 = 5 is obtained from some boundary complexes of 4simplices by a sequence of possible operations of types connected sums, bistellar 1 -moves, edge contractions, edge expansions, and an edge folding. As a result, K is a triangulation of either a sphere or a suspension of RP 2 . (c) 2024 Elsevier B.V. All rights reserved.