nLab Roman Mikhailov

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Selected writings

On combinatorial descriptions of homotopy groups of spheres:

• Roman Mikhailov, Jie Wu: A combinatorial description of homotopy groups of spheres [arXiv:1108.3055]

On fr-codes in homological algebra:

• Sergei O. Ivanov, Roman Mikhailov: A higher limit approach to homology theories, Journal of Pure and Applied Algebra 219 6 (2015) 1915-1939 [arXiv:1309.4920, doi:10.1016/j.jpaa.2014.07.016]

• Sergei O. Ivanov, Roman Mikhailov: Higher limits, homology theories and $\mathbf{fr}$-codes, in: Combinatorial and Toric Homotopy, Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore (2017) 229-261 [arXiv:1510.09044, doi:10.1142/9789813226579_0004]

• Sergei O. Ivanov, Roman Mikhailov, Fedor Pavutnitskiy: Limits, standard complexes and $\mathbf{fr}$-codes, Sb. Math. 211 (2020) 1568 [arXiv:1906.08793, doi:10.1070/SM9348, doi:10.1070/SM9348]

Proof that all higher homotopy groups of the 2-sphere are non-trivial:

• Sergei O. Ivanov, Roman Mikhailov, Jie Wu: On nontriviality of homotopy groups of spheres, Homology, Homotopy and Applications 18 2 (2016) [doi:10.4310/HHA.2016.v18.n2.a18, arXiv:1506.00952]

On aspects of group theory seen inside homotopy theory/$\infty$-group theory:

• Roman Mikhailov, Homotopy patterns in group theory, Proceedings of the ICM 2022 (arXiv:2111.00737)

Interview with Vladimir Voevodsky:

• Интервью Владимира Воеводского, Princeton 2012 (Part 1, Part 2)

category: people