A Lefschetz fixed point theorem in gravitational lensing
| dc.creator | Werner, Marcus C. | |
| dc.date | 2007-03-15 | |
| dc.date | 2007-05-17 | |
| dc.date.accessioned | 2026-07-07T08:01:55Z | |
| dc.date.available | 2026-07-07T08:01:55Z | |
| dc.description | Topological invariants play an important rôle in the theory of gravitational lensing by constraining the image number. Furthermore, it is known that, for certain lens models, the image magnifications $μ_i$ obey invariants of the form $\sum_i μ_i=1$. In this paper, we show that this magnification invariant is the holomorphic Lefschetz number of a suitably defined complexified lensing map, and hence a topological invariant. We also provide a heat kernel proof of the holomorphic Lefschetz fixed point formula which is central to this argument, based on Kotake's proof of the more general Atiyah-Bott theorem. Finally, we present a new astronomically motivated lens model for which this invariant holds. | |
| dc.description | 14 pages. Version 2: typos corrected | |
| dc.identifier | https://arxiv.org/abs/math-ph/0703050 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0703050 | |
| dc.identifier | J. Math. Phys. 48, 052501 (2007) | |
| dc.identifier | doi:10.1063/1.2735443 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/129066 | |
| dc.subject | Mathematical Physics | |
| dc.subject | Astrophysics | |
| dc.title | A Lefschetz fixed point theorem in gravitational lensing | |
| dc.type | text |