Existence and Non-Existence Results of Z2 Harmonic 1-Forms

Z2 harmonic 1-forms was introduced by Taubes as the boundary appearing in the compactification of the moduli space of flat SL(2,C) connections. Although from gauge theory aspect, Z2 harmonic 1-forms should exist widely, it is challenging to explicitly construct examples of them. Besides the curvature condition, there seems to have more obstruction of the existence of Z2 harmonic 1-forms. In this talk, we will discuss a method to construct examples of Z2 harmonic 1-forms. We will also discuss the relationship between Z2 harmonic 1-forms and special Lagrangian geometry and present a non-existence result based on the work of Abouzaid-Imagi.

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