The Morse Index of Redutible Solutions Of The Seiberg-Witten Equations
Celso Melchiades Doria

TL;DR
This paper derives a second variation formula for the Seiberg-Witten functional to estimate the Morse index of reducible solutions, showing it equals the dimension of a specific negative eigenspace, thus finite.
Contribution
It provides a new formula for the Morse index of reducible solutions of the Seiberg-Witten equations, linking it to spectral properties of a differential operator.
Findings
Morse index is finite for reducible solutions.
Morse index equals the dimension of the largest negative eigenspace of a specific operator.
Second variation formula for the Seiberg-Witten functional is established.
Abstract
The variation formula of the Seiberg-Witten functional is obtained in order to estimate the Morse index of redutible solutions . It is shown that their Morse index is given by the dimension of the largest negative eigenspace of the operator , hence it is finite.
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Taxonomy
TopicsTopological and Geometric Data Analysis · Nonlinear Waves and Solitons · Quantum chaos and dynamical systems
