Group actions, Teichmüller spaces and cobordisms
- Авторы: Apanasov B.1
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Учреждения:
- Department of Mathematics
- Выпуск: Том 38, № 2 (2017)
- Страницы: 213-228
- Раздел: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/198905
- DOI: https://doi.org/10.1134/S1995080217020032
- ID: 198905
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Аннотация
We discuss how the global geometry and topology of manifolds depend on different group actions of their fundamental groups, and in particular, how properties of a non-trivial compact 4-dimensional cobordism M whose interior has a complete hyperbolic structure depend on properties of the variety of discrete representations of the fundamental group of its 3-dimensional boundary ∂M. In addition to the standard conformal ergodic action of a uniformhyperbolic lattice on the round sphere Sn−1 and its quasiconformal deformations in Sn, we present several constructions of unusual actions of such lattices on everywhere wild spheres (boundaries of quasisymmetric embeddings of the closed n-ball into Sn), on non-trivial (n − 1)-knots in Sn+1, as well as actions defining non-trivial compact cobordisms with complete hyperbolic structures in its interiors. We show that such unusual actions always correspond to discrete representations of a given hyperbolic lattice from “non-standard” components of its varieties of representations (faithful or with large kernels of defining homomorphisms).
Об авторах
B. Apanasov
Department of Mathematics
Автор, ответственный за переписку.
Email: apanasov@ou.edu
США, Norman, OK, 73019