An index theorem for anti-self-dual orbifold-cone metrics

作者：Lock Michael T; Viaclovsky Jeff A^*

来源：Advances in Mathematics, 2013, 248: 698-716.

DOI：10.1016/j.aim.2013.08.004

• Anti-self-dual metrics
• Index theory
• Orbifolds

Recently, Atiyah and LeBrun proved versions of the Gauss-Bonnet and Hirzebruch signature theorems for metrics with edge-cone singularities in dimension four, which they applied to obtain an inequality of Hitchin-Thorpe type for Einstein edge-cone metrics. Interestingly, many natural examples of edge-cone metrics in dimension four are anti-self-dual (or self-dual depending upon choice of orientation). On such a space there is an important elliptic complex called the anti-self-dual deformation complex, whose index gives crucial information about the local structure of the moduli space of anti-self-dual metrics. In this paper, we compute the index of this complex in the orbifold case, and give several applications.

• 出版日期2013-11-25