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Russian Mathematical Surveys, 2019, Volume 74, Issue 3, Pages 461–524
DOI: https://doi.org/10.1070/RM9883 (Mi rm9883) 		 
This article is cited in 6 scientific papers (total in 6 papers)

$SU$-bordism: structure results and geometric representatives

I. Yu. Limonchenkoa, T. E. Panovbcd, G. Chernykhb

a National Research University Higher School of Economics
b Lomonosov Moscow State University
c Institute for Theoretical and Experimental Physics
d Institute for Information Transmission Problems of Russian Academy of Sciences
English version PDF (969 kB) Citations (6)
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DOI: https://doi.org/10.1070/RM9883
Abstract: The first part of this survey gives a modernised exposition of the structure of the special unitary bordism ring, by combining the classical geometric methods of Conner–Floyd, Wall, and Stong with the Adams–Novikov spectral sequence and formal group law techniques that emerged after the fundamental 1967 paper of Novikov. In the second part toric topology is used to describe geometric representatives in $SU$-bordism classes, including toric, quasi-toric, and Calabi–Yau manifolds.
Bibliography: 56 titles.
Keywords: special unitary bordism, $SU$-manifolds, Chern classes, toric varieties, quasi-toric manifolds, Calabi–Yau manifolds.
Funding agency Grant number
Russian Foundation for Basic Research 17-01-00671
18-51-50005
Simons Foundation
National Research University Higher School of Economics
Ministry of Education and Science of the Russian Federation 5-100
The research of the first author was carried out within the University Basic Research Program of the Higher School of Economics and was funded by the Russian Academic Excellence Project 5-100. The second and third authors were partially supported by the Russian Foundation for Basic Research (grant nos. 17-01-00671 and 18-51-50005). The second author was also supported by the Simons Foundation at the Independent University of Moscow.
Received: 18.03.2019
Russian version:
Uspekhi Matematicheskikh Nauk, 2019, Volume 74, Issue 3(447), Pages 95–166
DOI: https://doi.org/10.4213/rm9883
Bibliographic databases:
Document Type: Article
UDC: 515.14+515.16
MSC: Primary 55N22, 57R77; Secondary 55T15, 14M25, 14J32
Language: English
Original paper language: Russian
Citation: I. Yu. Limonchenko, T. E. Panov, G. Chernykh, “$SU$-bordism: structure results and geometric representatives”, Uspekhi Mat. Nauk, 74:3(447) (2019), 95–166; Russian Math. Surveys, 74:3 (2019), 461–524
Citation in format AMSBIB
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    • This publication is cited in the following 6 articles:
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