Weinstein presentations for high-dimensional antisurgery

TL;DR

This paper introduces an algorithm for describing Weinstein presentations of high-dimensional Weinstein subdomains, generalizing previous 3D work and introducing a new Legendrian isotopy move called the 'boat move.'

Contribution

It provides a novel algorithm and a new Legendrian isotopy move to describe Weinstein subdomains obtained by carving out regular Lagrangians in higher dimensions.

Findings

Developed an algorithm for Weinstein presentations in high dimensions.

Introduced the 'boat move' Legendrian isotopy for local index changes.

Described presentations for exotic Weinstein subdomains and explicit P-loose Legendrians.

Abstract

In this paper, we give an algorithm for describing the Weinstein presentation of Weinstein subdomains obtained by carving out regular Lagrangians. Our work generalizes previous work in dimension three and requires a novel Legendrian isotopy move (the ``boat move") that changes the local index of Reeb chords in a front projection. As applications, we describe presentations for certain exotic Weinstein subdomains and give explicit descriptions of $P$-loose Legendrians.