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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| Дата: | 2019 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2019
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| Назва видання: | Український математичний вісник |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/169429 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-169429 |
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dspace |
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irk-123456789-1694292020-06-14T01:26:19Z Hyperbolic topology and bounded locally homeomorphic quasiregular mappings in 3-space Apanasov, B.N. 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. 2019 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/169429 en Український математичний вісник Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Apanasov, B.N. |
| spellingShingle |
Apanasov, B.N. Hyperbolic topology and bounded locally homeomorphic quasiregular mappings in 3-space Український математичний вісник |
| author_facet |
Apanasov, B.N. |
| author_sort |
Apanasov, B.N. |
| title |
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_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_sort |
hyperbolic topology and bounded locally homeomorphic quasiregular mappings in 3-space |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2019 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/169429 |
| 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. |
| series |
Український математичний вісник |
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2023-10-18T22:25:10Z |
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2023-10-18T22:25:10Z |
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1796155466562142208 |