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Elliptic boundary value problem on non-compact $G$-manifolds

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arxiv 1602.00565 v2 pith:ETFQ544P submitted 2016-02-01 math.DG math.SG

classification math.DGmath.SG
keywords non-compacttypeatiyah-patodi-singerboundaryellipticgroupindexmanifold
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In this paper, an equality between the Hochs-Mathai type index and the Atiyah-Patodi-Singer type index is established when the manifold and the group action are both non-compact, which generalizes a result of Ma and Zhang for compact group actions. As a technical preparation, a problem concerning the Fredholm property of the global elliptic boundary value problems of the Atiyah-Patodi-Singer type on a non-compact manifold is studied.

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