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Canonical geometrization of 3-manifolds realizable as small coversстатья
- Автор: Ероховец Н.Ю.
- Сборник: ArXiv
- Серия: Series arxive "math"
- Том: 2005
- Год издания: 2020
- Издательство: Cornell University Press
- Местоположение издательства: United States
- Первая страница: 1
- Последняя страница: 24
- Аннотация: Roughly speaking geometrization conjecture of W. Thurson (finally proved by G.~Perelman) says that any oriented 3-manifold can be canonically partitioned into pieces, which have a geometrical structure of one of the eight types. In the seminal paper by M. W.Davis and T.Januszkiewicz (1991) there is a sketch of the proof that such a decomposition exists for 3-manifolds realizable as small covers over simple 3-polytopes. It should be noted, that in this sketch the notion of a nontrivial 4-belts, which plays an important role in the decomposition, is not mentioned. Moreover, is can be shown that, in general, a decomposition of a 3-polytope along 4-belts may be done in many inequivalent ways. In this paper we present a solution to the following problem: to build an explicit canonical decomposition.
- Добавил в систему: Ероховец Николай Юрьевич