|Title||An $L^2$-index theorem for group actions of noncompact quotients|
|Presenter||Hang Wang (The University of Adelaide)|
|Session||Analysis and Partial Differential Equations|
Atiyah’s $L^2$-index theorem relates the index of an elliptic operator on a closed manifold to the $L^2$-index of the elliptic operator lifted to a covering space. The theorem is useful in the study of existence of nontrivial solutions for elliptic PDE on noncompact manifolds, for example, $L^2$-harmonic forms. In this talk, we consider a type of noncompact manifolds, so-called manifolds with regular exhaustion, introduced by Roe, and show that Atiyah’s $L^2$-index theorem still hold. This is joint work with Guoliang Yu and Dapeng Zhou.
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