Positive Braid Links with Infinitely Many Fillings
Honghao Gao, Linhui Shen, Daping Weng
Abstract
We prove that any positive braid Legendrian link not isotopic to a standard finite type link admits infinitely many exact Lagrangian fillings.
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Positive Braid Links with Infinitely Many Fillings
Authors
Abstract
We prove that any positive braid Legendrian link not isotopic to a standard finite type link admits infinitely many exact Lagrangian fillings.
Paper Structure
This paper contains 18 sections, 20 theorems, 57 equations.
Table of Contents
- Introduction
- DT Transformation and Infinitely Many Fillings
- Full Cyclic Rotation
- Donaldson-Thomas Transformation
- Aperiodic DT Yields Infinitely Many Lagrangian Fillings
- Infinitely Many Fillings for Infinite Type
- Preparation
- Case 1: k=2
- Case 2: k=1
- Case 3: k=0
- Proof of Proposition \ref{['Mainquiver']} for 3-strand braids
- Proof of Proposition \ref{['Mainquiver']} for braids of at least 4 strands
- Case 1: $(p,q) = (2,2)$
- Case 2: $(p,q) = (2,3)$
- Case 3: $(p,q) = (3,3)$
- ...and 3 more sections
Key Result
Lemma 2.2
For any braid word $\beta$, we have $\Phi_\mathsf{R}=\mathrm{DT}^{-2}$ on $\mathrm{Aug}\left(\Lambda_\beta\right)$.
Theorems & Definitions (49)
- Example 1.2
- Definition 1.3
- Remark 2.1
- Lemma 2.2
- proof
- Theorem 2.3
- proof
- Remark 2.4
- Theorem 2.5
- proof
- ...and 39 more