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OP-10203Status unassessedGeometry and topology

Structures in arboreal geometry · Question 5.3

Arborealization of singularities of Lagrangian skeleta · AIMPL workshop record

MSC 53D · Symplectic geometry, contact geometry

Editorial mapping of AIMPL list topic: Arborealization of singularities of Lagrangian skeleta. http://aimpl.org/arborlagrange/ Not an author-supplied MSC code.

Workshop record · status unassessedAs of 2026-09-10 source snapshot; not a current-status certificationSource & evidence ↓
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Problem statement

Is it possible to set up Floer theory with boundary on an arboreal skeleton? What are arboreal Lagrangian boundary conditions?

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Background

Workshop introduction

This page is intended to collect the problems arising from the AIM workshop, "Arborealization of singularities of Lagrangian skeleta."

Section context

The theory of arboreal spaces (or "arborifolds") offers a rich new geometry with many interesting questions. The theory also offers us a new language for presenting already useful or important structures from symplectic, differential, and complex geometry.

Question context

Boundary conditions in Floer theory are given by smooth Lagrangians equipped with local systems. As in the above question, the analogous data on an arboreal Lagrangian is a microlocal sheaf. We might hope to understand this analogy in a Floer-theoretic way.

Progress & source assessment

Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.

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References
  1. [1]Arborealization of singularities of Lagrangian skeleta · Original question link
  2. [2]AIMPL source bibliography link
  3. [3]AIMPL text license · CC BY-SA 3.0 linkAIM Problem Lists (AIMPL), original contributors; CC BY-SA 3.0. Adaptation: structural TeX converted to Markdown, documented source macros expanded, and source bibliography links added. Mathematical wording retained. These adapted source texts remain under CC BY-SA 3.0.

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