Foliations and contact structures

• Applicants: Dr. Jonathan Bowden; Professor Dr. Thomas Vogel
• Subject Area: Mathematics
• Term: from 2014 to 2018
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 262521153

The goal of this project is to improve our understanding of the relationship between contact structures and foliations on closed 3-dimensional manifolds. Both structures are given in terms of plane fields with certain geometric properties. While it is known, due to work of Eliashberg and Thurston, that any foliation, with one exception, can be approximated by contact structures and after work of T. Vogel it is also known under which conditions the foliation determines the contact structures up to isotopy, many questions remain open.We want to-find interesting sufficient conditions on tight contact structures which imply that the contact structure can be obtained by approximation of a taut foliation, and- describe how the topology of the space of contact structures changes when one adds taut foliations or confoliations.

• DFG Programme: Research Grants