Lickorish-type Construction of Manifolds Over Simple Polytopes

Abstract

This paper is a survey on the Lickorish-type construction of some kind of closed manifolds over simple convex polytopes. Inspired by Lickorish’s theorem, we propose a method to describe certain families of manifolds over simple convex polytopes with torus action. Under this construction, many known classification results of these families of manifolds can be interpreted by this construction. Some further problems will be discussed in the end.