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Izv. RAN. Ser. Mat., 2000, Volume 64, Issue 2, Pages 3–28 (Mi izv282)  

This article is cited in 1 scientific paper (total in 2 paper)

The index of an equivariant vector field and addition theorems for Pontryagin classes

V. M. Buchstaber, K. E. Feldman

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: In this paper we construct a theory of indices of Morse–Bott vector fields on a manifold and use it to solve a famous localization problem for the transfer map. As a consequence, we obtain addition theorems for universal Pontryagin classes in cobordisms. This enables us to complete the construction of the theory of universal characteristic classes, which was begun more than twenty years ago.

DOI: https://doi.org/10.4213/im282

Full text: PDF file (2202 kB)
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English version:
Izvestiya: Mathematics, 2000, 64:2, 223–247

Bibliographic databases:

Document Type: Article
MSC: 55N22, 55P60, 55P91, 55R10, 55R12, 55R99
Received: 29.01.1999

Citation: V. M. Buchstaber, K. E. Feldman, “The index of an equivariant vector field and addition theorems for Pontryagin classes”, Izv. RAN. Ser. Mat., 64:2 (2000), 3–28; Izv. Math., 64:2 (2000), 223–247

Citation in format AMSBIB
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\pages 3--28
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\pages 223--247
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. A. Bolibrukh, A. P. Veselov, A. B. Zhizhchenko, I. M. Krichever, A. A. Mal'tsev, S. P. Novikov, T. E. Panov, Yu. M. Smirnov, “Viktor Matveevich Buchstaber (on his 60th birthday)”, Russian Math. Surveys, 58:3 (2003), 627–635  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. Saeki O., “Fold maps on 4-manifolds”, Comment. Math. Helv., 78:3 (2003), 627–647  crossref  mathscinet  zmath  isi  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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