An introduction to Weinstein handlebodies for complements of smoothed toric divisors

TL;DR

This paper introduces an algorithm for constructing Weinstein handlebodies for complements of smoothed toric divisors, providing explicit examples and diagrams to aid newcomers in understanding Weinstein handlebody techniques.

Contribution

It presents a new algorithm for constructing Weinstein handlebodies in the context of smoothed toric divisors, with explicit coordinate methods and illustrative examples.

Findings

Algorithm successfully constructs Weinstein handlebodies for specific cases.

Explicit examples demonstrate the effectiveness of the approach.

Provides accessible introduction to Weinstein handlebody diagrams and Kirby calculus.

Abstract

In this article, we provide an introduction to an algorithm for constructing Weinstein handlebodies for complements of certain smoothed toric divisors using explicit coordinates and a simple example. This article also serves to welcome newcomers to Weinstein handlebody diagrams and Weinstein Kirby calculus. Finally, we include one complicated example at the end of the article to showcase the algorithm and the types of Weinstein Kirby diagrams it produces.