Detect duality obstruction of calibrations in smooth category

TL;DR

This paper introduces new gluing techniques for calibrations, analyzes Lawlor cones' calibration support, and extends previous work on duality obstructions in smooth categories, revealing limitations of smooth calibrations.

Contribution

It presents a novel gluing result, characterizes Lawlor cones' calibration support, and advances understanding of duality obstructions in smooth calibrations.

Findings

New gluing method simplifies calibration extensions

Lawlor cones can support coflat calibrations singular only at the origin

Many Lawlor cones cannot support smooth calibrations

Abstract

This paper consists of three parts: (a) exhibit a new gluing result which can dramatically simplify extensions of calibration pairs; (b) observe that every Lawlor cone can support coflat calibrations singular only at the origin; (c) show that there exist many Lawlor cones which cannot support any smooth calibrations. As an application, we extend our previous work on detecting duality obstruction of calibrations in the smooth category.