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Lickorish-type Construction of Manifolds Over Simple Polytopes

  • Zhi LüEmail author
  • Wei Wang
  • Li Yu
Conference paper
Part of the Trends in Mathematics book series (TM)

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.

Notes

Acknowledgements

The authors are very grateful to the referees for carefully reading this manuscript and providing some very valuable and helpful suggestions.

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Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.School of Mathematical SciencesFudan UniversityShanghaiPeople’s Republic of China
  2. 2.College of Information TechnologyShanghai Ocean UniversityShanghaiPeople’s Republic of China
  3. 3.Department of Mathematics and IMSNanjing UniversityNanjingPeople’s Republic of China

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