# Lickorish type construction of manifolds over simple polytopes

## TL;DR

This paper surveys a method inspired by Lickorish's theorem for constructing and classifying certain closed manifolds with torus actions over simple convex polytopes.

## Contribution

It introduces a Lickorish type construction framework for manifolds over simple polytopes, connecting classical classification results within this approach.

## Key findings

- Provides a unified construction method for manifolds over simple polytopes
- Interprets classical classification results through the construction
- Discusses open problems related to the construction

## 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 classical classification results of these families of manifolds could be interpreted by this construction and some further problems will be discussed.