Lagrangian correspondences and pullbacks of virtual fundamental classes

TL;DR

This paper proposes that Lagrangian correspondences provide the appropriate framework for understanding the functoriality of virtual fundamental classes in the context of $-2$-symplectic derived structures.

Contribution

It introduces Lagrangian correspondences as the key conceptual tool for studying the functoriality of virtual fundamental classes in derived symplectic geometry.

Findings

Lagrangian correspondences effectively encode functoriality properties.

The framework applies to virtual fundamental classes in $-2$-symplectic derived structures.

Provides a new perspective on the relationship between symplectic geometry and derived algebraic geometry.

Abstract

We argue that Lagrangian correspondences are the correct framework to study functoriality of virtual fundamental classes arising from a $-2$-symplectic derived structure.