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 Tr. Mat. Inst. Steklova, 2018, Volume 302, Pages 57–97 (Mi tm3927)

This article is cited in 4 scientific papers (total in 4 papers)

Cobordisms, manifolds with torus action, and functional equations

V. M. Buchstaber

Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia

Abstract: The paper is devoted to applications of functional equations to well-known problems of compact torus actions on oriented smooth manifolds. These include the problem of Hirzebruch genera of complex cobordism classes that are determined by complex, almost complex, and stably complex structures on a fixed manifold. We consider actions with connected stabilizer subgroups. For each such action with isolated fixed points, we introduce rigidity functional equations. This is based on the localization theorem for equivariant Hirzebruch genera. We consider actions of maximal tori on homogeneous spaces of compact Lie groups and torus actions on toric and quasitoric manifolds. The arising class of equations contains both classical and new functional equations that play an important role in modern mathematical physics.

 Funding Agency Grant Number Russian Science Foundation 14-50-00005 This work is supported by the Russian Science Foundation under grant 14-50-00005.

DOI: https://doi.org/10.1134/S0371968518030044

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English version:
Proceedings of the Steklov Institute of Mathematics, 2018, 302, 48–87

Bibliographic databases:

UDC: 515.164.24+515.164.8+517.965
Received: May 18, 2018

Citation: V. M. Buchstaber, “Cobordisms, manifolds with torus action, and functional equations”, Topology and physics, Collected papers. Dedicated to Academician Sergei Petrovich Novikov on the occasion of his 80th birthday, Tr. Mat. Inst. Steklova, 302, MAIK Nauka/Interperiodica, Moscow, 2018, 57–97; Proc. Steklov Inst. Math., 302 (2018), 48–87

Citation in format AMSBIB
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This publication is cited in the following articles:
1. Ivan Yu. Limonchenko, Zhi Lü, Taras E. Panov, “Calabi–Yau hypersurfaces and SU-bordism”, Proc. Steklov Inst. Math., 302 (2018), 270–278
2. Elena Yu. Bunkova, “Hirzebruch functional equation: classification of solutions”, Proc. Steklov Inst. Math., 302 (2018), 33–47
3. I. Yu. Limonchenko, T. E. Panov, G. Chernykh, “$SU$-bordism: structure results and geometric representatives”, Russian Math. Surveys, 74:3 (2019), 461–524
4. E. Yu. Bunkova, “Universal Formal Group for Elliptic Genus of Level $N$”, Proc. Steklov Inst. Math., 305 (2019), 33–52
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