Hyperbolic topology and bounded locally homeomorphic quasiregular mappings in 3-space
| Autor: | Apanasov, Boris N. |
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| Rok vydání: | 2018 |
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| Druh dokumentu: | Working Paper |
| Popis: | We use our new type of bounded locally homeomorphic quasiregular mappings in the unit 3-ball to address long standing problems for such mappings. 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 $B^3\subset \mathbb{R}^3$ as mappings equivariant with the standard conformal action of uniform hyperbolic lattices $\Gamma\subset \operatorname{Isom} H^3$ in the unit 3-ball and with its discrete representation $G=\rho(\Gamma)\subset \operatorname{Isom} H^4 $. Here $G$ is the fundamental group of our non-trivial hyperbolic 4-cobordism $M=(H^4\cup\Omega(G))/G$ and the kernel of the homomorphism $\rho\!:\! \Gamma\rightarrow G$ is a free group $F_3$ on three generators. Comment: Clarification of the previous submission. 13 pages, 2 figures. arXiv admin note: text overlap with arXiv:1510.08951, arXiv:1611.00432 |
| Databáze: | arXiv |
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