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Apanasov B. N. Hyperbolic topology and bounded locally homeomorphic quasiregular mappings in 3-space [Електронний ресурс] / B. N. Apanasov // Український математичний вісник. - 2019. - Т. 16, № 1. - С. 10-27. - Режим доступу: http://nbuv.gov.ua/UJRN/UMvis_2019_16_1_5 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 Matti Vuorinen injectivity problem. The construction of such mappings comes from our construction of nontrivial compact 4-dimensional cobordisms 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 <$E3~symbol <172>~R sup 3> as mappings equivariant with the standard conformal action of uniform hyperbolic lattices <$EGAMMA~symbol <172>~Isom sup 3> in the unit 3-ball and with its discrete representation = <$Erho ( GAMMA )~symbol <172>~Isom sup 4>. Here is the fundamental group of our nontrivial hyperbolic 4-cobordism = <$E( nothing sup 4 union OMEGA (~))> and the kernel of the homomorphism <$Erho~:~GAMMA~symbol О~> is a free group 3 on three generators.
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Apanasov B. N. Quasiregular Mappings and Discrete Group Actions [Електронний ресурс] / B. N. Apanasov // Український математичний вісник. - 2021. - Т. 18, № 4. - С. 441-465. - Режим доступу: http://nbuv.gov.ua/UJRN/UMvis_2021_18_4_3
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