An index theorem for anti-self-dual orbifold-cone metrics |
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Authors: | Michael T. Lock Jeff A. Viaclovsky |
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Affiliation: | Department of Mathematics, University of Wisconsin, Madison, WI 53706, United States |
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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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Keywords: | Anti-self-dual metrics Index theory Orbifolds |
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