Golodness and polyhedral products for two-dimensional simplicial complexes

Abstract

Abstract Golodness of two-dimensional simplicial complexes is studied through polyhedral products, and combinatorial and topological characterizations of Golodness of surface triangulations are given. An answer to the question of Berglund is also given so that there is a two-dimensional simplicial complex which is rationally Golod but not Golod over <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>ℤ</m:mi> <m:mo>/</m:mo> <m:mi>p</m:mi> </m:mrow> </m:math> {\mathbb{Z}/p} .