Download this article
 Download this article For screen
For printing
Recent Issues

Volume 24
Issue 4, 1809–2387
Issue 3, 1225–1808
Issue 2, 595–1223
Issue 1, 1–594

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
Other MSP Journals
Weave-realizability for $D$–type

James Hughes

Algebraic & Geometric Topology 23 (2023) 2735–2776

We study exact Lagrangian fillings of Legendrian links of Dn–type in the standard contact 3–sphere. The main result is the existence of a Lagrangian filling, represented by a weave, such that any algebraic quiver mutation of the associated intersection quiver can be realized as a geometric weave mutation. The method of proof is via Legendrian weave calculus and a construction of appropriate 1–cycles whose geometric intersections realize the required algebraic intersection numbers. In particular, we show that, in D–type, each cluster chart of the moduli of microlocal rank-1 sheaves is induced by at least one embedded exact Lagrangian filling. Hence, the Legendrian links of Dn–type have at least as many Hamiltonian isotopy classes of Lagrangian fillings as cluster seeds in the Dn–type cluster algebra, and their geometric exchange graph for Lagrangian disk surgeries contains the cluster exchange graph of Dn–type.

Legendrian knots, exact Lagrangian fillings
Mathematical Subject Classification
Primary: 53D12
Secondary: 57K33
Received: 12 March 2021
Revised: 12 October 2021
Accepted: 22 March 2022
Published: 7 September 2023
James Hughes
Department of Mathematics
University of California, Davis
Davis, CA
United States

Open Access made possible by participating institutions via Subscribe to Open.