Weinstein handlebodies for complements of smoothed toric divisors / Bahar Acu, Orsola Capovilla-Searle, Agnès Gadbled, Aleksandra Marinlović, Emmy Murphy, Laura Starkston, Anglea Wu.

Format:

Book

Author/Creator:

Acu, Bahar, author.

Capovilla-Searle, Orsola, author.

Gadbled, Agnes, author.

Marinković, Aleksandra, 1966- author.

Murphy, Emmy, author.

Starkston, Laura, author.

Wu, Angela, author.

Series:

Memoirs of the American Mathematical Society; 1561 ; v.309.

Memoirs of the American Mathematical Society Series ; v. 309 ; n. 1561

Language:

English

Subjects (All):

Symplectic geometry.

Topology.

Physical Description:

v, 115 pages : illustrations ; 26 cm.

Place of Publication:

Providence, RI : American Mathematical Society, 2025.

Summary:

We study the interactions between toric manifolds and Weinstein handlebodies. We define a partially-centeredness condition on a Delzant polytope, which we prove ensures that the complement of a corresponding partial smoothing of the total toric divisor supports an explicit Weinstein structure. Many examples which fail this condition also fail to have Weinstein (or even exact) complement to the partially smoothed divisor. We investigate the combinatorial possibilities of Delzant polytopes that realize such Weinstein domain complements. We also develop an algorithm to construct a Weinstein handlebody diagram in Gompf standard form for the complement of such a partially smoothed total toric divisor. The algorithm we develop more generally outputs a Weinstein handlebody diagram for any Weinstein 4-manifold constructed by attaching 2-handles to the disk cotangent bundle of any suface F, where the 2-handles are attached along the co-oriented conormal lifts of curves on F. We discuss how to use these diagrams to calculate invariants and provide numerous examples applying this procedure. For example, we provide Weinstein handlebody diagrams for the complements of the smooth and nodal cubics in CP².

Contents:

Chapter 1. Introduction

Chapter 2. Weinstein domains and Kirby calculus

Chapter 3. Toric transformations

Chapter 4. Weinstein structure on the complement of a partially smoothed total toric divisor

Chapter 5. Combinatorial possibilities for Delzant polytopes and resulting Weinstein divisor complements

Chapter 6. Non-centered toric manifolds and obstructions

Chapter 7. Weinstein handlebody diagrams and cotangent bundles

Chapter 8. Lifting co-normals to Kirby diagrams

Chapter 9. Invariants

Chapter 10. Examples from the algorithm

Bibliography.

Notes:

"May 2025, volume 309, number 1561"

Includes bibliographical references (pages 113-115).

ISBN:

1470472708

9781470472702

OCLC:

1522469823