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The
relative $L^2$ index theorem for Galois coverings
Moulay-Tahar Benameur |
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Vol. 6 (2021), No. 3, 503–541
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Abstract |
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Given a Galois covering of complete spin manifolds where the base metric has positive scalar curvature near infinity, we prove that for small enough , the spectral projection of the Dirac operator has finite trace in the Atiyah von Neumann algebra. This allows us to define the index in the even case, and we prove its compatibility with the Xie–Yu higher index and deduce versions of the classical Gromov–Lawson relative index theorems. Finally, we briefly discuss some Gromov–Lawson invariants. |
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Keywords
$L^2$ index theorem, Galois covering, relative index,
Gromov–Lawson theorem, Dirac operator, complete manifold,
spin structure, positive scalar curvature
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Mathematical Subject Classification 2010
Primary: 32Q10, 53C27
Secondary: 53C12, 57R30
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Milestones
Received: 3 June 2020
Revised: 7 October 2020
Accepted: 4 January 2021
Published: 11 September 2021
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Authors |
| Moulay-Tahar Benameur | |
| Institut Montpellierain Alexander
Grothendieck Université de Montpellier Montpellier France |
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