A Seifert-van Kampen Theorem for Legendrian Submanifolds and Exact Lagrangian Cobordisms

TL;DR

This paper establishes a Seifert-van Kampen theorem for Legendrian submanifolds and exact Lagrangian cobordisms, enabling computation of DGA changes due to Legendrian ambient surgery, advancing understanding in symplectic topology.

Contribution

It introduces a novel Seifert-van Kampen theorem applicable to Legendrian and Lagrangian structures, facilitating new calculations in symplectic topology.

Findings

Proved a Seifert-van Kampen theorem for Legendrian submanifolds.

Calculated DGA changes caused by Legendrian ambient surgery.

Provided tools for analyzing Lagrangian cobordisms.

Abstract

We prove a Seifert-van Kampen theorem for Legendrian submanifolds and exact Lagrangian cobordisms, and use it to calculate the change in the DGA caused by critical Legendrian ambient surgery.