Small covers over wedges of polygons

Abstract

A small cover is a closed smooth manifold of dimension 𝑛 having a locally standard ℤ₂^𝑛-action whose orbit space is isomorphic to a simple polytope. In the paper, we classify small covers and real toric manifolds whose orbit space is isomorphic to the dual of the simplicial complex obtainable by a sequence of wedgings from a polygon, using a systematic combinatorial method of puzzles finding toric spaces.