Titre : | On the algebraic foundations of bounded cohomology | Type de document : | texte imprimé | Auteurs : | Theo BÜHLER, Auteur | Editeur : | Providence, R. I. [Etats Unis] : American Mathematical Society | Année de publication : | cop. 2011 | Collection : | Memoirs of the American Mathematical Society, ISSN 0065-9266 num. 1006 | Importance : | XXI-97 p. | ISBN/ISSN/EAN : | 978-0-8218-5311-5 | Langues : | Anglais (eng) | Catégories : | 18E30
| Mots-clés : | catégorie dérivée homologie espace topologique | Résumé : | Bounded cohomology for topological spaces was introduced by Gromov in the late seventies, mainly to describe the simplicial volume invariant. It is an exotic cohomology theory for spaces in that it fails excision and thus cannot be represented by spectra. Gromov's basic vanishing result of bounded cohomology for simply connected spaces implies that bounded cohomology for spaces is an invariant of the fundamental group. To prove this, one is led to introduce a cohomology theory for groups and the present work is concerned with the latter, which has been studied by Gromov, Brooks, Ivanov and Noskov to name but the most important initial contributors. Generalizing these ideas from discrete groups to topological groups, Burger and Monod have developed continuous bounded cohomology in the late nineties. | Note de contenu : | bibliogr. |
On the algebraic foundations of bounded cohomology [texte imprimé] / Theo BÜHLER, Auteur . - American Mathematical Society, cop. 2011 . - XXI-97 p.. - ( Memoirs of the American Mathematical Society, ISSN 0065-9266; 1006) . ISBN : 978-0-8218-5311-5 Langues : Anglais ( eng) Catégories : | 18E30
| Mots-clés : | catégorie dérivée homologie espace topologique | Résumé : | Bounded cohomology for topological spaces was introduced by Gromov in the late seventies, mainly to describe the simplicial volume invariant. It is an exotic cohomology theory for spaces in that it fails excision and thus cannot be represented by spectra. Gromov's basic vanishing result of bounded cohomology for simply connected spaces implies that bounded cohomology for spaces is an invariant of the fundamental group. To prove this, one is led to introduce a cohomology theory for groups and the present work is concerned with the latter, which has been studied by Gromov, Brooks, Ivanov and Noskov to name but the most important initial contributors. Generalizing these ideas from discrete groups to topological groups, Burger and Monod have developed continuous bounded cohomology in the late nineties. | Note de contenu : | bibliogr. |
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