Hyperbolic topology and bounded locally homeomorphic quasiregular mappings in 3-space
- Autores: Apanasov B.1
-
Afiliações:
- Department of Mathematics, University of Oklahoma
- Edição: Volume 242, Nº 6 (2019)
- Páginas: 760-771
- Seção: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/243038
- DOI: https://doi.org/10.1007/s10958-019-04514-4
- ID: 243038
Citar
Resumo
We use our new type of bounded locally homeomorphic quasiregular mappings in the unit 3-ball to address long standing problems for such mappings, including the Vuorinen injectivity problem. The construction of such mappings comes from our construction of non-trivial compact 4-dimensional cobordisms M with symmetric boundary components and whose interiors have complete 4-dimensional real hyperbolic structures. Such bounded locally homeomorphic quasiregular mappings are defined in the unit 3-ball B3 ⊂ ℝ3 as mappings equivariant with the standard conformal action of uniform hyperbolic lattices Γ ⊂ Isom H3 in the unit 3-ball and with its discrete representation G = ρ(Γ) ⊂ Isom H4. Here, G is the fundamental group of our non-trivial hyperbolic 4-cobordism M = (H4 ∪ Ω(G))/G, and the kernel of the homomorphism ρ: Γ → G is a free group F3 on three generators.
Sobre autores
Boris Apanasov
Department of Mathematics, University of Oklahoma
Autor responsável pela correspondência
Email: apanasov@ou.edu
Estados Unidos da América, Norman