Arkiv för Matematik

Volume 56 (2018)

Number 2

A simple construction of positive loops of Legendrians

Pages: 377 – 394



Dishant Pancholi (Institute for Mathematical Sciences, Taramani, Chennai, India)

José Luis Pérez (Instituto de Ciencias Matemáticas, Madrid, Spain)

Francisco Presas (Instituto de Ciencias Matemáticas, Madrid, Spain)


We construct positive loops of Legendrian submanifolds in several instances. In particular, we partially recover $G$. Liu’s result stating that any loose Legendrian admits a positive loop, under some mild topological assumptions on the Legendrian. Moreover, we show contractibility of the constructed loops under an extra topological assumption.

2010 Mathematics Subject Classification

Primary 53D10. Secondary 57R17.

Received 4 October 2017

Received revised 23 January 2018

Accepted 17 April 2018

Published 24 May 2022