Abstract
We describe the structure of the coefficient ring \(W^*(pt)=\varOmega_W^*\) of the \(c_1\)-spherical bordism theory for an arbitrary \(SU\)-bilinear multiplication. We prove that for any \(SU\)-bilinear multiplication the formal group of the theory \(W^*\) is Landweber exact. Also we show that after inverting the set \(\mathcal{P}\) of Fermat primes there exists a complex orientation of the localized theory \(W^*[\mathcal{P}^{-1}]\) such that the coefficients of the corresponding formal group law generate the whole coefficient ring \(\varOmega_W^*[\mathcal{P}^{-1}]\).
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Acknowledgments
The author is deeply grateful to Taras Panov for suggesting the problem, fruitful discussions, and constant attention to the work.
Funding
This research was carried out at the Steklov International Mathematical Center under the financial support of the Ministry of Science and Higher Education of the Russian Federation (agreement no. 075-15-2022-265). The author is supported by Theoretical Physics and Mathematics Advancement Foundation “BASIS”. The article was prepared within the framework of the HSE University Basic Research Program.
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Translated from Matematicheskie Zametki, 2023, Vol. 113, pp. 918–928 https://doi.org/10.4213/mzm13845.
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Chernykh, G.S. Landweber Exactness of the Formal Group Law in \(c_1\)-Spherical Bordism. Math Notes 113, 850–858 (2023). https://doi.org/10.1134/S0001434623050267
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DOI: https://doi.org/10.1134/S0001434623050267