Hyperbolic topology and bounded locally homeomorphic quasiregular mappings in 3-space
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...
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| Published in: | Український математичний вісник |
|---|---|
| Date: | 2019 |
| Main Author: | |
| Format: | Article |
| Language: | English |
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Інститут прикладної математики і механіки НАН України
2019
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/169429 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Hyperbolic topology and bounded locally homeomorphic quasiregular mappings in 3-space / B.N. Apanasov // Український математичний вісник. — 2019. — Т. 16, № 1. — С. 10-27. — Бібліогр.: 26 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862577554192334848 |
|---|---|
| author | Apanasov, B.N. |
| author_facet | Apanasov, B.N. |
| citation_txt | Hyperbolic topology and bounded locally homeomorphic quasiregular mappings in 3-space / B.N. Apanasov // Український математичний вісник. — 2019. — Т. 16, № 1. — С. 10-27. — Бібліогр.: 26 назв. — англ. |
| collection | DSpace DC |
| container_title | Український математичний вісник |
| description | 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 Г ⊂ IsomH³ in the unit 3-ball and with its discrete representation G = ρ(Г) ⊂ IsomH⁴. 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: Г → G is a free group F₃ on three generators.
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| first_indexed | 2025-11-26T15:34:35Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-169429 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1810-3200 |
| language | English |
| last_indexed | 2025-11-26T15:34:35Z |
| publishDate | 2019 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Apanasov, B.N. 2020-06-13T08:18:40Z 2020-06-13T08:18:40Z 2019 Hyperbolic topology and bounded locally homeomorphic quasiregular mappings in 3-space / B.N. Apanasov // Український математичний вісник. — 2019. — Т. 16, № 1. — С. 10-27. — Бібліогр.: 26 назв. — англ. 1810-3200 2000 MSC. 30C65, 57Q60, 20F55, 32T99, 30F40, 32H30, 57M30 https://nasplib.isofts.kiev.ua/handle/123456789/169429 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 Г ⊂ IsomH³ in the unit 3-ball and with its discrete representation G = ρ(Г) ⊂ IsomH⁴. 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: Г → G is a free group F₃ on three generators. en Інститут прикладної математики і механіки НАН України Український математичний вісник Hyperbolic topology and bounded locally homeomorphic quasiregular mappings in 3-space Article published earlier |
| spellingShingle | Hyperbolic topology and bounded locally homeomorphic quasiregular mappings in 3-space Apanasov, B.N. |
| title | Hyperbolic topology and bounded locally homeomorphic quasiregular mappings in 3-space |
| title_full | Hyperbolic topology and bounded locally homeomorphic quasiregular mappings in 3-space |
| title_fullStr | Hyperbolic topology and bounded locally homeomorphic quasiregular mappings in 3-space |
| title_full_unstemmed | Hyperbolic topology and bounded locally homeomorphic quasiregular mappings in 3-space |
| title_short | Hyperbolic topology and bounded locally homeomorphic quasiregular mappings in 3-space |
| title_sort | hyperbolic topology and bounded locally homeomorphic quasiregular mappings in 3-space |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/169429 |
| work_keys_str_mv | AT apanasovbn hyperbolictopologyandboundedlocallyhomeomorphicquasiregularmappingsin3space |