An abstract index theorem on non-compact Riemannian manifolds

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Article on an abstract index theorem on non-compact Riemannian manifolds.

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15 p.

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Anghel, Nicolae 1993.

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Article on an abstract index theorem on non-compact Riemannian manifolds.

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15 p.

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Abstract: We prove an abstract index theorem for essentially self-adjoint Fredholm supersymmetric first-order elliptic differential operators on Hermitian vector bundles over complete oriented Riemannian manifolds. According to our main result the supersymmetric L2-index of such an operator can be expressed as the sum of a "local contribution" (the familiar Atiyah-Singer index form, suitably restricted to and integrated over a finite region) and a "boundary contribution" (which depends only on the restriction of the operator at large distances). This is done by splicing together local parametrices and Green's operators defined "at infinity". The result yields (in fact is equivalent to) a generalisation of the relative index theorem of Gromov and Lawson.

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  • Houston Journal of Mathematics, 1993, Houston: University of Houston. Houston Journal of Mathematics, pp. 223-237

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  • Publication Title: Houston Journal of Mathematics
  • Volume: 19
  • Page Start: 223
  • Page End: 237
  • Peer Reviewed: Yes

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  • 1993

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  • May 16, 2013, 10:39 a.m.

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  • Nov. 18, 2014, 9:44 a.m.

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Anghel, Nicolae. An abstract index theorem on non-compact Riemannian manifolds, article, 1993; [Houston, Texas]. (digital.library.unt.edu/ark:/67531/metadc159527/: accessed December 13, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT College of Arts and Sciences.