July 30, 2025

Morse Index Stability for Yang–Mills Connections

MGMario GauvritCentre National de la Recherche Scientifique PLPaul LaurainUniversité Gustave Eiffel

Key Points

The sum of the morse index and nullity is asymptotically bounded by the weak limit and bubbles.
In dimension 4, the morse index is shown to have upper and lower bounds under weak convergence conditions.
The findings are based on an analysis of weak converging sequences of yang-mills connections.
This research highlights the significance of understanding stability in the context of gauge theory.

Abstract

Abstract We prove stability results for the Morse index plus nullity of Yang–Mills connections in dimension 4 under weak convergence. Precisely we establish that the sum of the Morse index and the nullity of a bounded sequence of Yang–Mills connections is asymptotically bounded above by the sum of the Morse index and the nullity of the weak limit and the bubbles, while the Morse index is asymptotically bounded below by the sum of the Morse index of the weak limit and the bubbles.

Ask AI

Helpful

Bookmark

View Full Paper