Index theorem for Z/2-harmonic spinors

Abstract

In my previous paper, I prove the existence of the Kuranishi structure for the moduli space $\mathfrak{M}$ of zero loci of $\mathbb{Z}/2$-harmonic spinors on a 3-manifold. So a nature question we can ask is to compute the virtual dimension for this moduli space ${\mathfrak{M}}_{g_0}:=\mathfrak{M}\cap \{g=g_0\}$. In this paper, I will first prove that $v-dim({\mathfrak{M}}_{g_0})=0$. Secondly, I will generalize this formula on 4-manifolds by using a special type of index developed by Jochen Bruning, Robert Seeley, and Fangyun Yang.

References in corpus (4)

• The zero loci of Z/2 harmonic spinors in dimension 2, 3 and 4
• On the behavior of sequences of solutions to U(1) Seiberg-Witten systems in dimension 4
• The behavior of sequences of solutions to the Vafa-Witten equations
• Seiberg-Witten monopoles with multiple spinors on a surface times a circle

Cited by in corpus (1)

• Examples of singularity models for $\mathbb{Z}/2$ harmonic 1-forms and spinors in dimension 3