Index theorem for Z/2-harmonic spinors

2017/05/04 by Takahashi, Ryosuke · 1 citation
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1705.01954

Abstract

In my previous paper, I prove the existence of the Kuranishi structure for the moduli space \mathfrakM of zero loci of 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 \mathfrakM_g0:=\mathfrakM∩\g=g₀\. In this paper, I will first prove that v-dim(\mathfrakM_g0)=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.

Cited by

• Perturbation and Pruning of Nondegenerate ℤ/2 Harmonic 1-forms

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