Adiabatic limits of co-associative Kovalev-Lefschetz fibrations

TL;DR

This paper investigates the behavior of co-associative fibrations in G_{2}-manifolds under adiabatic limits, proposing a local model involving maximal submanifolds in indefinite signature spaces and establishing global constructions.

Contribution

It introduces a new perspective on adiabatic limits of co-associative fibrations, linking them to maximal submanifolds in indefinite signature spaces and developing global frameworks.

Findings

Proposes a local model for adiabatic limits involving maximal submanifolds.

Establishes global constructions for co-associative fibrations.

Provides insights into the geometric structure of G_{2}-manifolds.

Abstract

We study co-associative fibrations of G_{2}-manifolds. We propose that the adiabatic limit of this structure should be given locally by a maximal submanifold in a space of indefinite signature and set up global versions of the constructions.