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Uspekhi Mat. Nauk, 2019, Volume 74, Issue 3(447), Pages 95–166 (Mi umn9883)  

$SU$-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

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.


DOI: https://doi.org/10.4213/rm9883

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English version:
Russian Mathematical Surveys, 2019, 74:3, 461–524

Bibliographic databases:

UDC: 515.14+515.16
MSC: Primary 55N22, 57R77; Secondary 55T15, 14M25, 14J32
Received: 18.03.2019

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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\pages 95--166
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\jour Russian Math. Surveys
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