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Mosc. Math. J., 2011, Volume 11, Number 1, Pages 139–147 (Mi mmj414)  

This article is cited in 8 scientific papers (total in 8 papers)

On rigid Hirzebruch genera

Oleg R. Musin

Department of Mathematics, University of Texas at Brownsville, Brownsville, TX

Abstract: The classical multiplicative (Hirzebruch) genera of manifolds have the wonderful property which is called rigidity. Rigidity of a genus $h$ means that if a compact connected Lie group $G$ acts on a manifold $X$, then the equivariant genus $h^G(X)$ is independent on $G$, i.e., $h^G(X)=h(X)$.
In this paper we are considering the rigidity problem for stably complex manifolds. In particular, we are proving that a genus is rigid if and only if it is a generalized Todd genus.

Key words and phrases: Hirzebruch genus, rigid genus, complex bordism.

DOI: https://doi.org/10.17323/1609-4514-2011-11-1-139-147

Full text: http://www.ams.org/.../abst11-1-2011.html
References: PDF file   HTML file

Bibliographic databases:

MSC: 55N22, 57R77
Received: February 11, 2009; in revised form July 10, 2010
Language:

Citation: Oleg R. Musin, “On rigid Hirzebruch genera”, Mosc. Math. J., 11:1 (2011), 139–147

Citation in format AMSBIB
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\by Oleg~R.~Musin
\paper On rigid Hirzebruch genera
\jour Mosc. Math.~J.
\yr 2011
\vol 11
\issue 1
\pages 139--147
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\crossref{https://doi.org/10.17323/1609-4514-2011-11-1-139-147}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2808215}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000286528100006}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. M. Buchstaber, I. V. Netay, “Hirzebruch Functional Equation and Elliptic Functions of Level $d$”, Funct. Anal. Appl., 49:4 (2015), 239–252  mathnet  crossref  crossref  isi  elib
    2. O. R. Musin, “Circle Actions with Two Fixed Points”, Math. Notes, 100:4 (2016), 636–638  mathnet  crossref  crossref  mathscinet  isi  elib
    3. A. Dessai, “Torus actions, fixed-point formulas, elliptic genera and positive curvature”, Front. Math. China, 11:5, SI (2016), 1151–1187  crossref  mathscinet  zmath  isi  scopus
    4. A. Weber, “Equivariant Hirzebruch class for singular varieties”, Sel. Math.-New Ser., 22:3 (2016), 1413–1454  crossref  mathscinet  zmath  isi  scopus
    5. Weber A., “Hirzebruch Class and Bia Lynicki-Birula Decomposition”, Transform. Groups, 22:2 (2017), 537–557  crossref  mathscinet  zmath  isi  scopus
    6. I. V. Netay, “Hirzebruch Functional Equations and Krichever Complex Genera”, Math. Notes, 103:2 (2018), 232–242  mathnet  crossref  crossref  isi  elib
    7. Z. Lü, O. R. Musin, “Rigidity of powers and Kosniowski's conjecture”, Sib. elektron. matem. izv., 15 (2018), 1227–1236  mathnet  crossref
    8. Elena Yu. Bunkova, “Hirzebruch functional equation: classification of solutions”, Proc. Steklov Inst. Math., 302 (2018), 33–47  mathnet  crossref  crossref  isi  elib
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