Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4665971 | Advances in Mathematics | 2013 | 19 Pages |
Abstract
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.
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Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Michael T. Lock, Jeff A. Viaclovsky,