RUS  ENG ЖУРНАЛЫ   ПЕРСОНАЛИИ   ОРГАНИЗАЦИИ   КОНФЕРЕНЦИИ   СЕМИНАРЫ   ВИДЕОТЕКА   ЛИЧНЫЙ КАБИНЕТ
Главная страница
О проекте
Программное обеспечение
Классификаторы
Полезные ссылки
Пользовательское
соглашение

Поиск публикаций
Поиск ссылок

RSS
Текущие выпуски
Архивные выпуски
Что такое RSS






Персональный вход:
Логин:
Пароль:
Запомнить пароль
Войти
Забыли пароль?
Регистрация


Int. Math. Res. Not. IMRN, 2013, выпуск 6, страницы 1324–1403 (Mi imrn6)  

Toric genera of homogeneous spaces and their fibrations

V. M. Buchstaberab, S. Terzićc

a Steklov Mathematical Institute, Russian Academy of Sciences, Gubkina Street 8, 119991 Moscow, Russia
b School of Mathematics, University of Manchester, Oxford Road, Manchester M13 9PL, UK
c Faculty of Science, University of Montenegro, Džordža Vašingtona bb, 81000 Podgorica, Montenegro

Аннотация: The aim of this paper is to further study the universal toric genus of compact homogeneous spaces and their homogeneous fibrations. We consider the homogeneous spaces with positive Euler characteristic. It is well known that such spaces carry many stable complex structures equivariant under the canonical action of the maximal torus $T^k$. As the torus action in this case only has isolated fixed points it is possible to effectively apply localization formula for the universal toric genus. Using this, we prove that the famous topological results related to rigidity and multiplicativity of a Hirzebruch genus can be obtained on homogeneous spaces just using representation theory. In this context, for homogeneous $SU$-spaces, we prove the well-known result about rigidity of the Krichever genus. We also prove that for a large class of stable complex homogeneous spaces any $T^k$-equivariant Hirzebruch genus given by an odd-power series vanishes. With regard to the problem of multiplicativity, we provide construction of stable complex $T^k$-fibrations for which the universal toric genus is twistedly multiplicative. We prove that it is always twistedly multiplicative for almost complex homogeneous fibrations and describe those fibrations for which it is multiplicative. As a consequence for such fibrations the strong relations between rigidity and multiplicativity for an equivariant Hirzebruch genus is established. The universal toric genus of the fibrations for which the base does not admit any stable complex structure is also considered. The main examples here for which we compute the universal toric genus are the homogeneous fibrations over quaternionic projective spaces.

DOI: https://doi.org/10.1093/imrn/rns022


Реферативные базы данных:

Тип публикации: Статья
Поступила в редакцию: 28.02.2011
Исправленный вариант: 15.12.2011
Принята в печать:24.01.2012
Язык публикации: английский

Образцы ссылок на эту страницу:
  • http://mi.mathnet.ru/imrn6

    ОТПРАВИТЬ: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Просмотров:
    Эта страница:30

     
    Обратная связь:
     Пользовательское соглашение  Регистрация  Логотипы © Математический институт им. В. А. Стеклова РАН, 2019