Volume 48, Issue 2 p. 173-241
Survey

Brieskorn manifolds in contact topology

Myeonggi Kwon

Myeonggi Kwon

Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, Building 27, Room 402, San 56-1, Sillim-dong, Gwanak-gu, Seoul 151-747, South Korea, [email protected]

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Otto van Koert

Corresponding Author

Otto van Koert

Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, Building 27, Room 402, San 56-1, Sillim-dong, Gwanak-gu, Seoul 151-747, South Korea, [email protected]

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First published: 14 January 2016
Citations: 36

2010 Mathematics Subject Classification 57R17, 57R58, 53D35, 53D40 (primary).

During this research Myeonggi Kwon and Otto van Koert were partially supported by the NRF Grant 2012-011755 funded by the Korean government. Otto van Koert was also partially supported by a stipend from the Humboldt foundation.

Abstract

In this survey, we give an overview of Brieskorn manifolds and varieties, and their role in contact topology. We discuss open books, fillings and invariants such as contact and symplectic homology. We also present some new results involving exotic contact structures, invariants and orderability. The main tool for the required computations is a version of the Morse–Bott spectral sequence. We provide a proof for the particular version that is useful for us.