A User's Guide to Morse Foliated Open Books

TL;DR

This paper explores Morse foliated open books as a tool for studying contact manifolds with boundary, extending the concept of right-veering to detect overtwistedness, and highlighting the advantages of the Morse perspective.

Contribution

It introduces the Morse foliated open books framework and extends the right-veering concept to this setting, aiding in the detection of overtwisted contact structures.

Findings

Morse foliated open books effectively study contact manifolds with boundary.

Extension of right-veering concept to Morse foliated open books.

Morse perspective offers advantages over previous methods.

Abstract

Morse foliated open books were introduced by the autors (along with abstract and embedded versions) as a tool for studying contact manifolds with boundary, and this article illustrates the advantages of the Morse perspective. We use this to extend the definition of \textit{right-veering} to foliated open books and we show that it plays a similar role in detecting overtwistedness as in other versions of open books.