Relative Donaldson-Thomas theory for Calabi-Yau 4-folds

TL;DR

This paper develops a theory of relative Donaldson-Thomas invariants for Calabi-Yau 4-folds with a Calabi-Yau 3-fold divisor, including gluing formulas linking these invariants to DT4 invariants.

Contribution

It introduces a new framework for relative DT invariants in the context of Calabi-Yau 4-folds and establishes gluing formulas connecting these to DT4 invariants.

Findings

Defined relative DT invariants for Calabi-Yau 4-folds with divisors.

Derived gluing formulas relating relative invariants to DT4 invariants.

Explored the cohomological aspects of the invariants.

Abstract

Given a complex 4-fold $X$ with an (Calabi-Yau 3-fold) anti-canonical divisor $Y$, we study relative Donaldson-Thomas invariants for this pair, which are elements in the Donaldson-Thomas cohomologies of $Y$. We also discuss gluing formulas which relate relative invariants and $DT_{4}$ invariants for Calabi-Yau 4-folds.