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New examples of Z2-harmonic 1-forms and their deformations

par Haydys, Andriy ;Mazzeo, Rafe;Takahashi, Ryosuke
Référence Geometriae dedicata, 219, 2, 30
Publication Publié, 2025-04-01

Article révisé par les pairs

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Résumé :

We collect a number of elementary constructions of Z2 harmonic 1-forms, and of families of these objects. These examples show that the branching set Σ of a Z2 harmonic 1-form may exhibit the following features: (i) Σ may be a non-trivial link; (ii) Σ may be a multiple cover; (iii) Σ may be immersed, and appear as a limit of smoothly embedded branching loci; (iv) there are families of Z2 harmonic 1-forms whose branching sets Σ have tangent cones filling out a positive dimensional space, even modulo isometries. We show that Features (i) and (ii) occur already in dimension three, while the remaining ones appear at least in dimension four and higher.