Toffoli, Enrico (2022) THE ATIYAH-PATODI-SINGER RHO INVARIANT AND SIGNATURES OF LINKS. PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 65 (2). pp. 404-440. ISSN 0013-0915, 1464-3839
Full text not available from this repository. (Request a copy)Abstract
Relations between the Atiyah-Patodi-Singer rho invariant and signatures of links have been known for a long time, but they were only partially investigated. In order to explore them further, we develop a versatile cut-and-paste formula for the rho invariant, which allows us to manipulate manifolds in a convenient way. With the help of this tool, we give a description of the multivariable signature of a link L as the rho invariant of some closed three-manifold Y-L intrinsically associated with L. We study then the rho invariant of the manifolds obtained by the Dehn surgery on L along integer and rational framings. Inspired by the results of Casson and Cordon and Cimasoni and Florens, we give formulas expressing this value as a sum of the multivariable signature of L and some easy-to-compute extra terms.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | SPECTRAL ASYMMETRY; MASLOV INDEX; CONCORDANCE; MANIFOLDS; rho invariant; aps; Atiyah-Patodi-Singer; Levine-Tristram; Cimasoni-Florens; multivariable signature; cut-and-paste; Dehn surgery |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 07 Feb 2024 06:57 |
| Last Modified: | 07 Feb 2024 06:57 |
| URI: | https://pred.uni-regensburg.de/id/eprint/56503 |
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