Spherical CR Dehn surgeries
| Autor: | Miguel Acosta |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Pure mathematics
figure eight knot General Mathematics 010102 general mathematics Structure (category theory) Holonomy Figure-eight knot spherical CR (G X)-structures Mathematics::Geometric Topology 01 natural sciences Dehn surgery 0103 physical sciences Mathematics [G03] [Physical chemical mathematical & earth Sciences] CR manifold Mathématiques [G03] [Physique chimie mathématiques & sciences de la terre] 010307 mathematical physics 0101 mathematics Element (category theory) Mathematics::Symplectic Geometry Complement (set theory) Mathematics |
| Zdroj: | Pacific Journal of Mathematics, 284(2), 257-282. Berkeley, CA: University of California at Berkeley (2016). |
| ISSN: | 0030-8730 |
| DOI: | 10.2140/pjm.2016.284.257 |
| Popis: | Consider a three dimensional cusped spherical CR manifold M and suppose that the holonomy representation of $\pi_1(M)$ can be deformed in such a way that the peripheral holonomy is generated by a non-parabolic element. We prove that, in this case, there is a spherical CR structure on some Dehn surgeries of M. The result is very similar to R. Schwartz's spherical CR Dehn surgery theorem, but has weaker hypotheses and does not give the uniformizability of the structure. We apply our theorem in the case of the Deraux-Falbel structure on the Figure Eight knot complement and obtain spherical CR structures on all Dehn surgeries of slope $-3 + r$ for $r \in \mathbb{Q}^{+}$ small enough. |
| Databáze: | OpenAIRE |
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