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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2024, Volume 325, Pages 81–92
DOI: https://doi.org/10.4213/tm4389 (Mi tm4389) 		 
Todd Polynomials and Hirzebruch Numbers

V. M. Buchstaberab, A. P. Veselovc

a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, 119991 Russia
b Lomonosov Moscow State University, Moscow, 119991 Russia
c Department of Mathematical Sciences, Loughborough University, Loughborough, LE11 3TU, UK
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DOI: https://doi.org/10.4213/tm4389
Abstract: In 1956 Hirzebruch found an explicit formula for the denominators of the Todd polynomials, which was proved later in his joint work with Atiyah. We present a new formula for the Todd polynomials in terms of the “forgotten symmetric functions,” which follows from our previous work on complex cobordisms. In particular, this leads to a simpler proof of the Hirzebruch formula and provides new interpretations for the Hirzebruch numbers.
Keywords: Todd polynomials, Hirzebruch numbers, symmetric functions.
Funding agency
This work was supported by ongoing institutional funding. No additional grants to carry out or direct this particular research were obtained.
Received: November 13, 2023
Revised: January 28, 2024
Accepted: March 11, 2024
English version:
Proceedings of the Steklov Institute of Mathematics, 2024, Volume 325, Pages 74–85
DOI: https://doi.org/10.1134/S0081543824020044
Document Type: Article
UDC: 515.14
Language: Russian
Citation: V. M. Buchstaber, A. P. Veselov, “Todd Polynomials and Hirzebruch Numbers”, Geometry, Topology, and Mathematical Physics, Collected papers. Dedicated to Academician Sergei Petrovich Novikov on the occasion of his 85th birthday, Trudy Mat. Inst. Steklova, 325, Steklov Mathematical Institute of RAS, Moscow, 2024, 81–92; Proc. Steklov Inst. Math., 325 (2024), 74–85
Citation in format AMSBIB
\Bibitem{BucVes24}
\by V.~M.~Buchstaber, A.~P.~Veselov
\paper Todd Polynomials and Hirzebruch Numbers
\inbook Geometry, Topology, and Mathematical Physics
\bookinfo Collected papers. Dedicated to Academician Sergei Petrovich Novikov on the occasion of his 85th birthday
\serial Trudy Mat. Inst. Steklova
\yr 2024
\vol 325
\pages 81--92
\publ Steklov Mathematical Institute of RAS
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4389}
\crossref{https://doi.org/10.4213/tm4389}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2024
\vol 325
\pages 74--85
\crossref{https://doi.org/10.1134/S0081543824020044}
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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