Multiple Derived Lagrangian Intersections

TL;DR

This paper introduces a novel method for constructing Lagrangian submanifolds within shifted symplectic derived stacks by utilizing multiple intersections and fiber products, expanding the toolkit for symplectic geometry.

Contribution

It presents a new approach to generate Lagrangians via multiple fiber products in shifted symplectic derived stacks, highlighting a cyclic product structure.

Findings

m-fold fiber product of Lagrangians is Lagrangian in a cyclic product

Provides a new construction method for Lagrangians in derived stacks

Enhances understanding of intersection theory in shifted symplectic geometry

Abstract

We give a new way to produce examples of Lagrangians in shifted symplectic derived stacks, based on multiple intersections. Specifically, we show that an m-fold fiber product of Lagrangians in a shifted symplectic derived stack its itself Lagrangian in a certain cyclic product of pairwise homotopy fiber products of the Lagrangians.