Surgery induces exact sequences in Lagrangian cobordisms

TL;DR

This paper demonstrates that surgery operations on Lagrangian branes induce exact sequences in the category of Lagrangian cobordisms, linking geometric modifications to algebraic structures.

Contribution

It establishes a fiber sequence in Lagrangian cobordisms induced by surgery on intersecting exact branes, extending known results to wrapped and exact settings.

Findings

Existence of fiber sequences from surgery on Lagrangian branes.

Extension of Biran and Cornea's results to new settings.

Connections between geometric surgeries and algebraic exact sequences.

Abstract

We prove that if L_0 and L_1 are exact branes intersecting in precisely one point, then there exists a fiber sequence in the infinity-category of Lagrangian cobordisms consisting of L_0, L_1, and a surgery of L_0 with L_1. By combining this with the exact functor from [Tan], we find analogues of results of Biran and Cornea in the wrapped and exact setting.