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Almost flat bundles and almost flat structuresстатья
Информация о цитировании статьи получена из
Web of Science
Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 29 мая 2015 г.
- Авторы: Mishchenko A.S., Teleman N.
- Журнал: Topological methods in nonlinear analysis
- Том: 26
- Номер: 1
- Год издания: 2005
- Издательство: Juliusz Schauder Center
- Местоположение издательства: Toru∎, Poland
- Первая страница: 75
- Последняя страница: 87
- Аннотация: In this paper we discuss some geometric aspects concerning almost flat bundles, notion introduced by Connes, Gromov and Moscovici [2]. Using a natural construction of [1], we present here a simple description of such bundles. For this we modify the notion of almost flat structure on bundles over smooth manifolds and extend this notion to bundles over arbitrary CW-spaces using quasi-connections [3]. Connes, Gromov and Moscovici [2] showed that for any almost flat bundle alpha over the manifold M, the index of the signature operator with values in a is a homotopy equivalence invariant of M. From here it follows that a certain integer multiple n of the bundle a comes from the classifying space B pi(1)(M). The geometric arguments discussed in this paper allow us to show that the bundle a itself, and not necessarily a certain multiple of it, comes from an arbitrarily large compact subspace Y subset of B pi(1)(M) trough the classifying mapping.
- Добавил в систему: Мищенко Александр Сергеевич