An Abstract Index Theorem on Non-Compact Riemannian Manifolds

Description:

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

Creator(s): Anghel, Nicolae
Creation Date: 1993  
Partner(s):
UNT College of Arts and Sciences
Collection(s):
UNT Scholarly Works
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Past 30 days: 10
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Creator (Author):
Anghel, Nicolae

University of North Texas

Publisher Info:
Place of Publication: [Houston, Texas]
Date(s):
  • Creation: 1993
Description:

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

Degree:
Department: Mathematics
Note:

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.

Physical Description:

15 p.

Language(s):
Subject(s):
Keyword(s): Riemannian manifolds | abstract index theorem
Source: Houston Journal of Mathematics, 1993, Houston: University of Houston. Houston Journal of Mathematics, pp. 223-237
Partner:
UNT College of Arts and Sciences
Collection:
UNT Scholarly Works
Identifier:
  • ARK: ark:/67531/metadc159527
Resource Type: Article
Format: Text
Rights:
Access: Public
Citation:
Publication Title: Houston Journal of Mathematics
Volume: 19
Page Start: 223
Page End: 237
Peer Reviewed: Yes